[41C,42S] Linear Congruential Generator Programs that generate Binary OEIS sequences

[Allen]

Some basic Linear Congruental Generators that produce binary sequences from OEIS.
These should produce all "known", and may or may not diverge after that- though many are periodic and can be further optimized/explored.

• A000035 : Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n.
• A011558 : Expansion of (x + x^3)/(1 + x + ... + x^4) mod 2.
• A011655 : Period 3: repeat [0, 1, 1].
• A011656 : A binary m-sequence: expansion of reciprocal of x^3 + x^2 + 1 (mod 2), shifted by 2 initial 0's.
• A060584 : Compare ultimate and penultimate digits of n base 3, i.e., 0 if n mod 3 = floor(n/3) mod 3, 1 otherwise; also 0 if (n mod 9) is a multiple of 4, 1 otherwise.
• A074937 : Let c(1) = c(2) = 1, c(n+2) = 1/(c(n+1)+c(n)); then a(n) = (1+sign(c(n)-sqrt(1/2))/2.
• A079979 : Characteristic function of multiples of six.
• A079998 : The characteristic function of the multiples of five.
• A082848 : Duplicate of A078588 a(n) = 1 if the integer multiple of phi nearest n is greater than n, otherwise 0, where phi = (1+sqrt(5))/2.
• A088911 : Period 6: repeat [1, 1, 1, 0, 0, 0].
• A093719 : a(n) = (n mod 2)^(n mod 3).
• A094875 : a(n)=1 if floor(Pi*10^n) is prime, otherwise a(n)=0.
• A095130 : Expansion of (x+x^2)/(1-x^6); period 6: repeat [0, 1, 1, 0, 0, 0].
• A097325 : Period 6: repeat [0, 1, 1, 1, 1, 1].
• A098457 : Farey Bisection Expansion of sqrt(7).
• A100283 : a(n) = floor(p*(n+1)) - floor(p*(n)) - 1 where p = Padovan plastic number = 1.324718... (cf. A060006 "Decimal expansion of real root of x^3 - x - 1 (the plastic constant).
• A105563 : a(n) = if (exactly 4 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.
• A108357 : Expansion of (1+x^2+x^4)/(1-x^8).
• A109720 : Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.
• A115790 : 1 - (Floor((n+1)*Pi)-Floor(n*Pi)) mod 2.
• A121262 : The characteristic function of the multiples of four.
• A126565 : a(n) = ceiling(sin(n)*cos(n)).
• A131078 : Periodic sequence (1, 1, 1, 1, 0, 0, 0, 0).
• A131532 : Period 6: repeat [0, 0, 0, 0, 1, 1].
• A131719 : Period 6: repeat [0, 1, 1, 1, 1, 0].
• A131735 : Period 6: repeat [0, 0, 1, 1, 1, 1].
• A133872 : Period 4: repeat [1, 1, 0, 0].
• A141260 : a(n) = 1 if n == {0,1,3,4,5,7,9,11} mod 12, otherwise a(n) = 0.
• A144595 : Christoffel word of slope 4/7.
• A144596 : Christoffel word of slope 2/7.
• A144597 : Christoffel word of slope 3/7.
• A144598 : Christoffel word of slope 5/7.
• A144599 : Christoffel word of slope 6/7.
• A144600 : Christoffel word of slope 2/11.
• A144601 : Christoffel word of slope 3/11.
• A144602 : Christoffel word of slope 4/11.
• A144603 : Christoffel word of slope 5/11.
• A144604 : Christoffel word of slope 6/11.
• A144605 : Christoffel word of slope 7/11.
• A144606 : Christoffel word of slope 8/11.
• A144607 : Christoffel word of slope 9/11.
• A144608 : Christoffel word of slope 10/11.
• A145568 : Characteristic function of numbers relatively prime to 11.
• A152822 : Periodic sequence [1,1,0,1] of length 4.
• A165211 : Period 8: repeat [0,1,0,1,1,0,1,0].
• A166486 : Periodic sequence [0,1,1,1] of length 4.
• A168181 : Characteristic function of numbers that are not multiples of 8.
• A168182 : Characteristic function of numbers that are not multiples of 9.
• A168184 : Characteristic function of numbers that are not multiples of 10.
• A168185 : Characteristic function of numbers that are not multiples of 12.
• A171386 : The characteristic function of 2 and 3: 1 if n is prime such that either n-1 or n+1 is prime, else 0.
• A172051 : Decimal expansion of 1/999999.
• A173857 : Expansion of 3/2 in base phi.
• A179850 : Characteristic function of numbers that are congruent to {0, 1, 3, 4} mod 5.
• A185017 : Characteristic function of 7.
• A187074 : a(n) = 0 if and only if n is of the form 3*k or 4*k + 2, otherwise a(n) = 1.
• A191152 : [4n*e]-2[2n*e], where [ ]=floor.
• A195062 : Period 7: repeat [1, 0, 1, 0, 1, 0, 1].
• A204418 : Periodic sequence 1,0,1,..., arranged in a triangle.
• A232990 : Period 5: repeat [1,0,0,1,0].
• A232991 : Period 6: repeat [1, 0, 0, 0, 1, 0].
• A241979 : (0,1) sequence such that lengths of three consecutive runs are always distinct.
• A267142 : The characteristic function of the multiples of 9.
• A272532 : Single bit representation of the sum of two sinusoids with periods 2 and 2*sqrt(2).
• A283437 : Periodic {1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1}.
• A320106 : Möbius transform of A320107 a(n) = A001227(A252463(n)).
• A354354 : a(n) = 1 if n is neither a multiple of 2 nor 3, and otherwise 0.
  

A000035 : Period 2: repeat [0, 1]; a(n) = n mod 2; parity of n.

• Beginning: 01010101010101010101010101010101010101010101010101010101010101010101010101010101​01010101010101010101010101010101010101010101010101010101010101010101010101010101​0101010101010101010101010101010101010101
• Period: periodic with length 2
• Count: 1001
• Starting seed: 0
• Multiplier: 3
• Increment: 1
• MOD: 2
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A000035"
02 0
03 STO 00
04 1001
05 STO 01
06>LBL 00
07 RCL 00
08 3
09 ×
10 1
11 +
12 2
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A011558 : Expansion of (x + x^3)/(1 + x + ... + x^4) mod 2.

• Beginning: 01111011110111101111011110111101111011110111101111011110111101111011110111101111​01111011110111101111011110111101111011110111101111011110111101111011110111101111​0111101111011110111101111011110111101111
• Period: periodic with length 5
• Count: 65538
• Starting seed: 0
• Multiplier: 2
• Increment: 1
• MOD: 31
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A011558"
02 0
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 31
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A011655 : Period 3: repeat [0, 1, 1].

• Beginning: 01101101101101101101101101101101101101101101101101101101101101101101101101101101​1011011011011011011011011
• Period: periodic with length 3
• Count: 105
• Starting seed: 0
• Multiplier: 2
• Increment: 1
• MOD: 7
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A011655"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 7
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A011656 : A binary m-sequence: expansion of reciprocal of x^3 + x^2 + 1 (mod 2), shifted by 2 initial 0's.

• Beginning: 00101110010111001011100101110010111001011100101110010111001011100101110010111001​0111001011100101110010111
• Period: periodic with length 7
• Count: 105
• Starting seed: 12
• Multiplier: 6
• Increment: 5
• MOD: 29
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A011656"
02 12
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 6
09 ×
10 5
11 +
12 29
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A060584 : Compare ultimate and penultimate digits of n base 3, i.e., 0 if n mod 3 = floor(n/3) mod 3, 1 otherwise; also 0 if (n mod 9) is a multiple of 4, 1 otherwise.

• Beginning: 01110111001110111001110111001110111001110111001110111001110111001110111001110111​0011101110011101110011101
• Period: periodic with length 9
• Count: 105
• Starting seed: 0
• Multiplier: 4
• Increment: 1
• MOD: 73
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A060584"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 1
11 +
12 73
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A074937 : Let c(1) = c(2) = 1, c(n+2) = 1/(c(n+1)+c(n)); then a(n) = (1+sign(c(n)-sqrt(1/2))/2.

• Beginning: 00100100110110010010011011001001001101100100100110110010010011011001001001101100​1001101101100100110110110
• Period: aperiodic
• Count: 105
• Starting seed: 91
• Multiplier: 180
• Increment: 41
• MOD: 179
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A074937"
02 91
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 180
09 ×
10 41
11 +
12 179
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A079979 : Characteristic function of multiples of six.

• Beginning: 10000010000010000010000010000010000010000010000010000010000010000010000010000010​00001000001000001000001000001000001000001000001000001000001000001000001000001000​0010000010000010000010000010000010000010
• Period: periodic with length 6
• Count: 65539
• Starting seed: 5
• Multiplier: 4
• Increment: 1
• MOD: 13
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A079979"
02 5
03 STO 00
04 65539
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 1
11 +
12 13
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A079998 : The characteristic function of the multiples of five.

• Beginning: 10000100001000010000100001000010000100001000010000100001000010000100001000010000​10000100001000010000100001000010000100001000010000100001000010000100001000010000​1000010000100001000010000100001000010000
• Period: periodic with length 5
• Count: 16386
• Starting seed: 3
• Multiplier: 6
• Increment: 1
• MOD: 5
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A079998"
02 3
03 STO 00
04 16386
05 STO 01
06>LBL 00
07 RCL 00
08 6
09 ×
10 1
11 +
12 5
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A082848 : Duplicate of A078588 "a(n) = 1 if the integer multiple of phi nearest n is greater than n, otherwise 0, where phi = (1+sqrt(5))/2.

• Beginning: 01010010110100101101011010010110100101001011010010110101101001011010010100101101​0010110100101001011010010
• Period: periodic with length 13
• Count: 105
• Starting seed: 83
• Multiplier: 90
• Increment: 5
• MOD: 89
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A082848"
02 83
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 90
09 ×
10 5
11 +
12 89
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A088911 : Period 6: repeat [1, 1, 1, 0, 0, 0].

• Beginning: 11100011100011100011100011100011100011100011100011100011100011100011100011100011​1000111000111000111000111
• Period: periodic with length 6
• Count: 105
• Starting seed: 1
• Multiplier: 3
• Increment: 1
• MOD: 7
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A088911"
02 1
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 3
09 ×
10 1
11 +
12 7
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A093719 : a(n) = (n mod 2)^(n mod 3).

• Beginning: 11010111010111010111010111010111010111010111010111010111010111010111010111010111​01011101011101011101011101011101011101011101011101011101011101011101011101011101​0111010111010111010111010111010111010111
• Period: periodic with length 6
• Count: 65538
• Starting seed: 2
• Multiplier: 4
• Increment: 2
• MOD: 13
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A093719"
02 2
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 2
11 +
12 13
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A094875 : a(n)=1 if floor(Pi*10^n) is prime, otherwise a(n)=0.

• Beginning: 11000100000000000000000000000000000001000000000000000000000000000000000000000000​00000000000000000000
• Period: aperiodic
• Count: 100
• Starting seed: 192
• Multiplier: 157
• Increment: 97
• MOD: 263
• Bit value: (x >> 8) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A094875"
02 192
03 STO 00
04 100
05 STO 01
06>LBL 00
07 RCL 00
08 157
09 ×
10 97
11 +
12 263
13 MOD
14 STO 00
15 256
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A095130 : Expansion of (x+x^2)/(1-x^6); period 6: repeat [0, 1, 1, 0, 0, 0].

• Beginning: 01100001100001100001100001100001100001100001100001100001100001100001100001100001​1000011000011000011000011
• Period: periodic with length 6
• Count: 105
• Starting seed: 5
• Multiplier: 4
• Increment: 1
• MOD: 13
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A095130"
02 5
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 1
11 +
12 13
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A097325 : Period 6: repeat [0, 1, 1, 1, 1, 1].

• Beginning: 01111101111101111101111101111101111101111101111101111101111101111101111101111101​11110111110111110111110111110111110111110111110111110111110111110111110111110111​1101111101111101111101111101111101111101
• Period: periodic with length 6
• Count: 26245
• Starting seed: 0
• Multiplier: 11
• Increment: 5
• MOD: 37
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A097325"
02 0
03 STO 00
04 26245
05 STO 01
06>LBL 00
07 RCL 00
08 11
09 ×
10 5
11 +
12 37
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A098457 : Farey Bisection Expansion of sqrt(7).

• Beginning: 11010111101011110101111010111101011110101111010111101011110101111010111101011110​1011110101111010111101011
• Period: periodic with length 7
• Count: 105
• Starting seed: 15
• Multiplier: 16
• Increment: 13
• MOD: 29
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A098457"
02 15
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 16
09 ×
10 13
11 +
12 29
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A100283 : a(n) = floor(p*(n+1)) - floor(p*(n)) - 1 where p = Padovan plastic number = 1.324718... (cf. A060006 Decimal expansion of real root of x^3 - x - 1 (the plastic constant).

• Beginning: 00010010010010010010010010010010010010001001001001001001001001001001001001001000​1001001001001001001001001
• Period: aperiodic
• Count: 105
• Starting seed: 130
• Multiplier: 192
• Increment: 62
• MOD: 191
• Bit value: (x >> 7) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A100283"
02 130
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 192
09 ×
10 62
11 +
12 191
13 MOD
14 STO 00
15 128
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A105563 : a(n) = if (exactly 4 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.

• Beginning: 00010001000010000100010000100001000100001000100001000010001000010000100010000100​00100010000100001000
• Period: periodic with length 14
• Count: 100
• Starting seed: 20
• Multiplier: 164
• Increment: 35
• MOD: 163
• Bit value: (x >> 7) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A105563"
02 20
03 STO 00
04 100
05 STO 01
06>LBL 00
07 RCL 00
08 164
09 ×
10 35
11 +
12 163
13 MOD
14 STO 00
15 128
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A108357 : Expansion of (1+x^2+x^4)/(1-x^8).

• Beginning: 10101000101010001010100010101000101010001010100010101000101010001010100010101000​101010001010100010101
• Period: periodic with length 8
• Count: 101
• Starting seed: 0
• Multiplier: 14
• Increment: 3
• MOD: 41
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A108357"
02 0
03 STO 00
04 101
05 STO 01
06>LBL 00
07 RCL 00
08 14
09 ×
10 3
11 +
12 41
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A109720 : Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.

• Beginning: 01111110111111011111101111110111111011111101111110111111011111101111110111111011​1111011111101111110111111
• Period: periodic with length 7
• Count: 105
• Starting seed: 0
• Multiplier: 21
• Increment: 15
• MOD: 43
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A109720"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 21
09 ×
10 15
11 +
12 43
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A115790 : 1 - (Floor((n+1)*Pi)-Floor(n*Pi)) mod 2.

• Beginning: 00000001000000100000010000001000000100000010000001000000100000010000001000000100​0000100000010000001000000
• Period: periodic with length 1
• Count: 105
• Starting seed: 63
• Multiplier: 150
• Increment: 64
• MOD: 149
• Bit value: (x >> 7) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A115790"
02 63
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 150
09 ×
10 64
11 +
12 149
13 MOD
14 STO 00
15 128
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A121262 : The characteristic function of the multiples of four.

• Beginning: 10001000100010001000100010001000100010001000100010001000100010001000100010001000​10001000100010001000100010001000100010001000100010001000100010001000100010001000​1000100010001000100010001000100010001000
• Period: periodic with length 4
• Count: 65538
• Starting seed: 1
• Multiplier: 3
• Increment: 1
• MOD: 5
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A121262"
02 1
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 3
09 ×
10 1
11 +
12 5
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A126565 : a(n) = ceiling(sin(n)*cos(n)).

• Beginning: 01001001001001101101101100100100100110110110110010010010011011011011001001001001​1011011011001001001001101
• Period: aperiodic
• Count: 105
• Starting seed: 113
• Multiplier: 158
• Increment: 43
• MOD: 157
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A126565"
02 113
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 158
09 ×
10 43
11 +
12 157
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A131078 : Periodic sequence (1, 1, 1, 1, 0, 0, 0, 0).

• Beginning: 11110000111100001111000011110000111100001111000011110000111100001111000011110000​1111000011110000111100001
• Period: periodic with length 8
• Count: 105
• Starting seed: 7
• Multiplier: 2
• Increment: 1
• MOD: 17
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A131078"
02 7
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 17
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A131532 : Period 6: repeat [0, 0, 0, 0, 1, 1].

• Beginning: 00001100001100001100001100001100001100001100001100001100001100001100001100001100​0011000011000011000011000
• Period: periodic with length 6
• Count: 105
• Starting seed: 0
• Multiplier: 4
• Increment: 1
• MOD: 13
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A131532"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 1
11 +
12 13
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A131719 : Period 6: repeat [0, 1, 1, 1, 1, 0].

• Beginning: 01111001111001111001111001111001111001111001111001111001111001111001111001111001​1110011110011110011110011110
• Period: periodic with length 6
• Count: 108
• Starting seed: 0
• Multiplier: 8
• Increment: 4
• MOD: 19
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A131719"
02 0
03 STO 00
04 108
05 STO 01
06>LBL 00
07 RCL 00
08 8
09 ×
10 4
11 +
12 19
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A131735 : Period 6: repeat [0, 0, 1, 1, 1, 1].

• Beginning: 00111100111100111100111100111100111100111100111100111100111100111100111100111100​1111001111001111001111001
• Period: periodic with length 6
• Count: 105
• Starting seed: 0
• Multiplier: 8
• Increment: 4
• MOD: 19
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A131735"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 8
09 ×
10 4
11 +
12 19
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A133872 : Period 4: repeat [1, 1, 0, 0].

• Beginning: 11001100110011001100110011001100110011001100110011001100110011001100110011001100​11001100110011001100110011001100110011001100110011001100110011001100110011001100​1100110011001100110011001100110011001100
• Period: periodic with length 4
• Count: 10001
• Starting seed: 1
• Multiplier: 2
• Increment: 1
• MOD: 5
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A133872"
02 1
03 STO 00
04 10001
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 5
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A141260 : a(n) = 1 if n == {0,1,3,4,5,7,9,11} mod 12, otherwise a(n) = 0.

• Beginning: 10111010101110111010101110111010101110111010101110111010101110111010101110111010​1011101110101011101110101011
• Period: periodic with length 12
• Count: 108
• Starting seed: 46
• Multiplier: 81
• Increment: 29
• MOD: 97
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A141260"
02 46
03 STO 00
04 108
05 STO 01
06>LBL 00
07 RCL 00
08 81
09 ×
10 29
11 +
12 97
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144595 : Christoffel word of slope 4/7.

• Beginning: 00100100101001001001010010010010100100100101001001001010010010010100100100101001​0010010100100100101001001
• Period: periodic with length 11
• Count: 105
• Starting seed: 4
• Multiplier: 12
• Increment: 4
• MOD: 11
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144595"
02 4
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 12
09 ×
10 4
11 +
12 11
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144596 : Christoffel word of slope 2/7.

• Beginning: 00001000100001000100001000100001000100001000100001000100001000100001000100001000​1000010001000010001000010
• Period: periodic with length 9
• Count: 105
• Starting seed: 14
• Multiplier: 9
• Increment: 6
• MOD: 19
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144596"
02 14
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 9
09 ×
10 6
11 +
12 19
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144597 : Christoffel word of slope 3/7.

• Beginning: 00010010010001001001000100100100010010010001001001000100100100010010010001001001​0001001001000100100100010
• Period: periodic with length 10
• Count: 105
• Starting seed: 0
• Multiplier: 23
• Increment: 17
• MOD: 41
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144597"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 23
09 ×
10 17
11 +
12 41
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144598 : Christoffel word of slope 5/7.

• Beginning: 00101001010100101001010100101001010100101001010100101001010100101001010100101001​0101001010010101001010010
• Period: periodic with length 12
• Count: 105
• Starting seed: 31
• Multiplier: 29
• Increment: 7
• MOD: 37
• Bit value: (x >> 2) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144598"
02 31
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 29
09 ×
10 7
11 +
12 37
13 MOD
14 STO 00
15 4
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144599 : Christoffel word of slope 6/7.

• Beginning: 00101010101010010101010101001010101010100101010101010010101010101001010101010100​1010101010100101010101010
• Period: periodic with length 13
• Count: 105
• Starting seed: 11
• Multiplier: 14
• Increment: 1
• MOD: 13
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144599"
02 11
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 14
09 ×
10 1
11 +
12 13
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144600 : Christoffel word of slope 2/11.

• Beginning: 00000010000010000001000001000000100000100000010000010000001000001000000100000100​0000100000100000010000010
• Period: periodic with length 13
• Count: 105
• Starting seed: 107
• Multiplier: 14
• Increment: 3
• MOD: 157
• Bit value: (x >> 5) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144600"
02 107
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 14
09 ×
10 3
11 +
12 157
13 MOD
14 STO 00
15 32
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144601 : Christoffel word of slope 3/11.

• Beginning: 00001000010001000010000100010000100001000100001000010001000010000100010000100001​0001000010000100010000100
• Period: periodic with length 14
• Count: 105
• Starting seed: 44
• Multiplier: 23
• Increment: 19
• MOD: 71
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144601"
02 44
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 23
09 ×
10 19
11 +
12 71
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144602 : Christoffel word of slope 4/11.

• Beginning: 00010001000100100010001000100100010001000100100010001000100100010001000100100010​0010001001000100010001001
• Period: periodic with length 15
• Count: 105
• Starting seed: 77
• Multiplier: 85
• Increment: 2
• MOD: 151
• Bit value: (x >> 6) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144602"
02 77
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 85
09 ×
10 2
11 +
12 151
13 MOD
14 STO 00
15 64
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144603 : Christoffel word of slope 5/11.

• Beginning: 00010010010010010001001001001001000100100100100100010010010010010001001001001001​0001001001001001000100100
• Period: periodic with length 16
• Count: 105
• Starting seed: 40
• Multiplier: 115
• Increment: 37
• MOD: 97
• Bit value: (x >> 5) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144603"
02 40
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 115
09 ×
10 37
11 +
12 97
13 MOD
14 STO 00
15 32
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144604 : Christoffel word of slope 6/11.

• Beginning: 00100100100100101001001001001001010010010010010010100100100100100101001001001001​0010100100100100100101001
• Period: periodic with length 17
• Count: 105
• Starting seed: 124
• Multiplier: 133
• Increment: 51
• MOD: 137
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144604"
02 124
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 133
09 ×
10 51
11 +
12 137
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144605 : Christoffel word of slope 7/11.

• Beginning: 00100101001010010100100101001010010100100101001010010100100101001010010100100101​0010100101001001010010100
• Period: periodic with length 18
• Count: 105
• Starting seed: 72
• Multiplier: 158
• Increment: 61
• MOD: 157
• Bit value: (x >> 6) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144605"
02 72
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 158
09 ×
10 61
11 +
12 157
13 MOD
14 STO 00
15 64
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144606 : Christoffel word of slope 8/11.

• Beginning: 00101001010100101010010100101010010101001010010101001010100101001010100101010010​1001010100101010010100101
• Period: periodic with length 19
• Count: 105
• Starting seed: 8
• Multiplier: 20
• Increment: 8
• MOD: 19
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144606"
02 8
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 20
09 ×
10 8
11 +
12 19
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144607 : Christoffel word of slope 9/11.

• Beginning: 00101010100101010101001010101001010101010010101010010101010100101010100101010101​0010101010010101010100101
• Period: periodic with length 20
• Count: 105
• Starting seed: 0
• Multiplier: 106
• Increment: 56
• MOD: 241
• Bit value: (x >> 6) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144607"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 106
09 ×
10 56
11 +
12 241
13 MOD
14 STO 00
15 64
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A144608 : Christoffel word of slope 10/11.

• Beginning: 00101010101010101010100101010101010101010100101010101010101010100101010101010101​0101001010101010101010101
• Period: periodic with length 21
• Count: 105
• Starting seed: 152
• Multiplier: 168
• Increment: 8
• MOD: 167
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A144608"
02 152
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 168
09 ×
10 8
11 +
12 167
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A145568 : Characteristic function of numbers relatively prime to 11.

• Beginning: 01111111111011111111110111111111101111111111011111111110111111111101111111111011​1111111101111111111011111
• Period: periodic with length 11
• Count: 105
• Starting seed: 0
• Multiplier: 58
• Increment: 32
• MOD: 353
• Bit value: (x >> 5) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A145568"
02 0
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 58
09 ×
10 32
11 +
12 353
13 MOD
14 STO 00
15 32
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A152822 : Periodic sequence [1,1,0,1] of length 4.

• Beginning: 11011101110111011101110111011101110111011101110111011101110111011101110111011101​11011101110111011101110111011101110111011101110111011101110111011101110111011101​1101110111011101110111011101110111011101
• Period: periodic with length 4
• Count: 65538
• Starting seed: 3
• Multiplier: 8
• Increment: 3
• MOD: 13
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A152822"
02 3
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 8
09 ×
10 3
11 +
12 13
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A165211 : Period 8: repeat [0,1,0,1,1,0,1,0].

• Beginning: 01011010010110100101101001011010010110100101101001011010010110100101101001011010​01011010010110100101101001011010010110100101101001011010010110100101101001011010​0101101001011010010110100101101001011010
• Period: periodic with length 8
• Count: 1001
• Starting seed: 0
• Multiplier: 8
• Increment: 7
• MOD: 17
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A165211"
02 0
03 STO 00
04 1001
05 STO 01
06>LBL 00
07 RCL 00
08 8
09 ×
10 7
11 +
12 17
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A166486 : Periodic sequence [0,1,1,1] of length 4.

• Beginning: 01110111011101110111011101110111011101110111011101110111011101110111011101110111​01110111011101110111011101110111011101110111011101110111011101110111011101110111​0111011101110111011101110111011101110111
• Period: periodic with length 4
• Count: 65538
• Starting seed: 0
• Multiplier: 8
• Increment: 3
• MOD: 13
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A166486"
02 0
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 8
09 ×
10 3
11 +
12 13
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A168181 : Characteristic function of numbers that are not multiples of 8.

• Beginning: 01111111011111110111111101111111011111110111111101111111011111110111111101111111​01111111011111110111111101111111011111110111111101111111011111110111111101111111​0111111101111111011111110111111101111111
• Period: periodic with length 8
• Count: 16385
• Starting seed: 0
• Multiplier: 22
• Increment: 15
• MOD: 73
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A168181"
02 0
03 STO 00
04 16385
05 STO 01
06>LBL 00
07 RCL 00
08 22
09 ×
10 15
11 +
12 73
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A168182 : Characteristic function of numbers that are not multiples of 9.

• Beginning: 01111111101111111101111111101111111101111111101111111101111111101111111101111111​10111111110111111110111111110111111110111111110111111110111111110111111110111111​1101111111101111111101111111101111111101
• Period: periodic with length 9
• Count: 1000
• Starting seed: 0
• Multiplier: 16
• Increment: 6
• MOD: 109
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A168182"
02 0
03 STO 00
04 1000
05 STO 01
06>LBL 00
07 RCL 00
08 16
09 ×
10 6
11 +
12 109
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A168184 : Characteristic function of numbers that are not multiples of 10.

• Beginning: 01111111110111111111011111111101111111110111111111011111111101111111110111111111​01111111110111111111011111111101111111110111111111011111111101111111110111111111​0111111111011111111101111111110111111111
• Period: periodic with length 10
• Count: 1001
• Starting seed: 0
• Multiplier: 46
• Increment: 13
• MOD: 71
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A168184"
02 0
03 STO 00
04 1001
05 STO 01
06>LBL 00
07 RCL 00
08 46
09 ×
10 13
11 +
12 71
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A168185 : Characteristic function of numbers that are not multiples of 12.

• Beginning: 01111111111101111111111101111111111101111111111101111111111101111111111101111111​11110111111111110111111111110111111111110111111111110111111111110111111111110111​1111111101111111111101111111111101111111
• Period: periodic with length 12
• Count: 65538
• Starting seed: 0
• Multiplier: 89
• Increment: 45
• MOD: 229
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A168185"
02 0
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 89
09 ×
10 45
11 +
12 229
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A171386 : The characteristic function of 2 and 3: 1 if n is prime such that either n-1 or n+1 is prime, else 0.

• Beginning: 01100000000000000000000000000000000000000000000000000000000000000000000000000000​0000000000000000000000000
• Period: aperiodic
• Count: 105
• Starting seed: 97
• Multiplier: 2
• Increment: 1
• MOD: 131
• Bit value: (x >> 7) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A171386"
02 97
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 131
13 MOD
14 STO 00
15 128
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A172051 : Decimal expansion of 1/999999.

• Beginning: 00000100000100000100000100000100000100000100000100000100000100000100000100000100​0001000001000001000001000
• Period: periodic with length 6
• Count: 105
• Starting seed: 8
• Multiplier: 4
• Increment: 1
• MOD: 13
• Bit value: (x >> 3) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A172051"
02 8
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 1
11 +
12 13
13 MOD
14 STO 00
15 8
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A173857 : Expansion of 3/2 in base phi.

• Beginning: 10100100100100100100100100100100100100100100100100100100100100100100100100100100​1001001001001001001001001
• Period: aperiodic
• Count: 105
• Starting seed: 77
• Multiplier: 150
• Increment: 50
• MOD: 149
• Bit value: (x >> 6) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A173857"
02 77
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 150
09 ×
10 50
11 +
12 149
13 MOD
14 STO 00
15 64
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A179850 : Characteristic function of numbers that are congruent to {0, 1, 3, 4} mod 5.

• Beginning: 11011110111101111011110111101111011110111101111011110111101111011110111101111011​11011110111101111011110111101111011110111101111011110111101111011110111101111011​1101111011110111101111011110111101111011
• Period: periodic with length 5
• Count: 5000
• Starting seed: 3
• Multiplier: 2
• Increment: 1
• MOD: 31
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A179850"
02 3
03 STO 00
04 5000
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 31
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A185017 : Characteristic function of 7.

• Beginning: 00000001000000000000000000000000000000000000000000000000000000000000000000000000​0000000000000000000000
• Period: periodic with length 1
• Count: 102
• Starting seed: 12
• Multiplier: 8
• Increment: 1
• MOD: 131
• Bit value: (x >> 7) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A185017"
02 12
03 STO 00
04 102
05 STO 01
06>LBL 00
07 RCL 00
08 8
09 ×
10 1
11 +
12 131
13 MOD
14 STO 00
15 128
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A187074 : a(n) = 0 if and only if n is of the form 3*k or 4*k + 2, otherwise a(n) = 1.

• Beginning: 10011011001010011011001010011011001010011011001010011011001010011011001010011011​0010100110110010100110110
• Period: periodic with length 12
• Count: 105
• Starting seed: 24
• Multiplier: 7
• Increment: 3
• MOD: 73
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A187074"
02 24
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 7
09 ×
10 3
11 +
12 73
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A191152 : [4n*e]-2[2n*e], where [ ]=floor.

• Beginning: 01010100101010110101010010101011010101001010101101010100101010110101011010101001​010101101010100101010110101010010101011010101001010
• Period: periodic with length 16
• Count: 131
• Starting seed: 178
• Multiplier: 182
• Increment: 23
• MOD: 181
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A191152"
02 178
03 STO 00
04 131
05 STO 01
06>LBL 00
07 RCL 00
08 182
09 ×
10 23
11 +
12 181
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A195062 : Period 7: repeat [1, 0, 1, 0, 1, 0, 1].

• Beginning: 10101011010101101010110101011010101101010110101011010101101010110101011010101101​0101101010110101011010101101010110101011010101
• Period: periodic with length 7
• Count: 126
• Starting seed: 7
• Multiplier: 16
• Increment: 7
• MOD: 29
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A195062"
02 7
03 STO 00
04 126
05 STO 01
06>LBL 00
07 RCL 00
08 16
09 ×
10 7
11 +
12 29
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A204418 : Periodic sequence 1,0,1,..., arranged in a triangle.

• Beginning: 10110110110110110110110110110110110110110110110110110110110110110110110110110110​1101101101101101101101101
• Period: periodic with length 3
• Count: 105
• Starting seed: 1
• Multiplier: 2
• Increment: 1
• MOD: 7
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A204418"
02 1
03 STO 00
04 105
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 7
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A232990 : Period 5: repeat [1,0,0,1,0].

• Beginning: 10010100101001010010100101001010010100101001010010100101001010010100101001010010​100101001010010100101001010
• Period: periodic with length 5
• Count: 107
• Starting seed: 2
• Multiplier: 6
• Increment: 1
• MOD: 5
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A232990"
02 2
03 STO 00
04 107
05 STO 01
06>LBL 00
07 RCL 00
08 6
09 ×
10 1
11 +
12 5
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A232991 : Period 6: repeat [1, 0, 0, 0, 1, 0].

• Beginning: 10001010001010001010001010001010001010001010001010001010001010001010001010001010​001010001010001010001010001
• Period: periodic with length 6
• Count: 107
• Starting seed: 5
• Multiplier: 3
• Increment: 1
• MOD: 7
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A232991"
02 5
03 STO 00
04 107
05 STO 01
06>LBL 00
07 RCL 00
08 3
09 ×
10 1
11 +
12 7
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A241979 : (0,1) sequence such that lengths of three consecutive runs are always distinct.

• Beginning: 01100010011101100010011101100010011101100010011101100010011101100010011101100010​0111011000100111011000100111
• Period: periodic with length 12
• Count: 108
• Starting seed: 2
• Multiplier: 2
• Increment: 1
• MOD: 13
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A241979"
02 2
03 STO 00
04 108
05 STO 01
06>LBL 00
07 RCL 00
08 2
09 ×
10 1
11 +
12 13
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A267142 : The characteristic function of the multiples of 9.

• Beginning: 10000000010000000010000000010000000010000000010000000010000000010000000010000000​01000000001000000001000000001000000001000000001000000001000000001000000001000000​0010000000010000000010000000010000000010
• Period: periodic with length 9
• Count: 1000
• Starting seed: 8
• Multiplier: 4
• Increment: 3
• MOD: 19
• Bit value: (x >> 4) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A267142"
02 8
03 STO 00
04 1000
05 STO 01
06>LBL 00
07 RCL 00
08 4
09 ×
10 3
11 +
12 19
13 MOD
14 STO 00
15 16
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A272532 : Single bit representation of the sum of two sinusoids with periods 2 and 2*sqrt(2).

• Beginning: 10110110100100101101101101001001011011011010010010110110100100100101101101001001​0010110110100100101101101101001001011011
• Period: periodic with length 3
• Count: 120
• Starting seed: 0
• Multiplier: 182
• Increment: 53
• MOD: 181
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A272532"
02 0
03 STO 00
04 120
05 STO 01
06>LBL 00
07 RCL 00
08 182
09 ×
10 53
11 +
12 181
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A283437 : Periodic {1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1}.

• Beginning: 11110100101111110100101111110100101111110100101111110100101111110100101111110100​1011111101001011111101001011
• Period: periodic with length 12
• Count: 108
• Starting seed: 59
• Multiplier: 81
• Increment: 9
• MOD: 97
• Bit value: (x >> 0) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A283437"
02 59
03 STO 00
04 108
05 STO 01
06>LBL 00
07 RCL 00
08 81
09 ×
10 9
11 +
12 97
13 MOD
14 STO 00
15 1
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A320106 : Möbius transform of A320107 a(n) = A001227(A252463(n)).

• Beginning: 10001110001010001110001010001110001010001110001010001110001010001110001010001110​00101000111000101000111000101000111000101000111000101000111000101000111000101000​1110001010001110001010001110001010001110
• Period: periodic with length 12
• Count: 65537
• Starting seed: 16
• Multiplier: 14
• Increment: 8
• MOD: 37
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A320106"
02 16
03 STO 00
04 65537
05 STO 01
06>LBL 00
07 RCL 00
08 14
09 ×
10 8
11 +
12 37
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

A354354 : a(n) = 1 if n is neither a multiple of 2 nor 3, and otherwise 0.

• Beginning: 01000101000101000101000101000101000101000101000101000101000101000101000101000101​00010100010100010100010100010100010100010100010100010100010100010100010100010100​0101000101000101000101000101000101000101
• Period: periodic with length 6
• Count: 65538
• Starting seed: 6
• Multiplier: 3
• Increment: 1
• MOD: 7
• Bit value: (x >> 1) & 1
  

42s Program (not optimized, byte count a place holder and not correct)

Code:


00 { 44-Byte Prgm }
01>LBL "A354354"
02 6
03 STO 00
04 65538
05 STO 01
06>LBL 00
07 RCL 00
08 3
09 ×
10 1
11 +
12 7
13 MOD
14 STO 00
15 2
16 /
17 1
18 AND
19 PRX
20 DSE 01
21 GTO 00
22 .END.

[rprosperi]

Epic post Allen (the longest I've ever seen) ! It's not only rich with information on all kinds of these sequences, they all also include code that folks can simply copy/paste to emulators or devices to test and explore the listed and related sequences.

Thank you very much for all the work, patience and diligence to create and share this with the community!!