(38G) OEIS A262389: Last Digit Composite

[Gerald H]

The programme inserts symbolics in the Sequence App to produce the sequence of numbers having right-most digit composite.

For more info please see

https://oeis.org/A262389

Code:

RECURSE(U,U2(N-2),4,6)►U1(N):
CHECK 1:
RECURSE(U,U3(N-2),8,9)►U2(N):
RECURSE(U,U3(N-1)+U2(N-2)-U1(N-1),14,16)►U3(N):

[Gerald H]

The 3 recursions can be telescoped into one, producing a faster method of generating the series.

Code:

RECURSE(U,IFTE(N>5,U1(N-1)+U1(N-4)-U1(N-5),IFTE(N==5,14,IFTE(N==4,9,8))),4,6)►U1(N):
CHECK 1:

Although I find the first version more pretty.

[Didier Lachieze]

Here is a direct formula tested on the Prime as I don't have a 38G:

Code:

U(N)=10*IP((N-1)/4)+2*(N MOD 4)+7*NOT(N MOD 4)+2

[Gerald H]

Bravo Didier!

On 38G you must have brackets around (NOT(N MOD 4)) then it works OK.

I tried a formula, but yours beats mine.

Here's mine:

Code:

RECURSE(U,(5*N+1-U2(N)+(3+U2(N))*U2((2*N-3-U2(N))/4)/2)/2,4,6)►U1(N):
CHECK 1:
RECURSE(U,IFTE(N MOD 2,-1,1),-1,1)►U2(N):

just for the record.

[Gerald H]

Explicitly, this is what Didier's formula should look like on the 38G:

Code:

RECURSE(U,(10*INT((N-1)/4)+2*(N MOD 4)+7*NOT N MOD 4)+2
,4,6) ►U1(N):
CHECK 1:

[Gerald H]

Didier, perhaps you should inform OEIS of your formula, as it's more elegant than any on their webpage.