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+--- Thread: (33s): OEIS A1614, Connell sequence, & A122793, A171152, A118011 (/thread-18596.html)
(33s): OEIS A1614, Connell sequence, & A122793, A171152, A118011 - Gerald H - 07-28-2022 11:34 AM
Takes a real integer from the stack & returns A118011(N)
https://oeis.org/A118011
, A171152(N)
https://oeis.org/A171152
,A122793(N)
https://oeis.org/A122793
& A1614(N)
https://oeis.org/A001614
to stack.
Nth member of complement of Connell sequence & partial sum, Nth of Connell sequence & partial sum of series.
eg For input
2022
The programme returns
T: 4,108 Complement of Connell sequence, 2022nd number not in Connell sequence
Z: 4,176,234 Sum of first 2022 members of Complement sequence
Y: 3,980 2022nd member of Connell sequence
X: 4,004,778 Sum of first 2022 members of Connell sequence
Code:
1. LBL M
2. STO N
3. IP(SQRT(2)*SQRT(N)+0.5)
4. STO E
5. E*(N+(1-SQ(E))/6)
6. STO F
7. N+SQ(N)
8. STO G
9. 2*N+E
10. G+F
11. 2*N-E
12. G-F
13. RTN
M: LN = 102RE: (33s): OEIS A1614, Connell sequence, & A122793, A171152, A118011 - John Keith - 07-28-2022 07:52 PM
That is an impressively small program, especially considering that it returns all 4 values. But then I noticed your name on the formulas on the OEIS pages.
Here is a program for the HP 49 and 50 using ListExt 1.3 which works in a completely different way. Given a number n on the stack, the program returns a list of the first n*(n+1)/2 terms of the Connell sequence A001614. With an input of 50, the program returns a list of 1275 numbers in about 2.1 seconds on my 50g.
Code:
\<< LSEQ
{ DUP 1 - SQ 1 + 2 ROT LASEQ
} LMAP LXIL
\>>For the partial sums A122793, follow the program with { + } LSCAN.