A124456 Numbers n which divide the sum of the Fibonacci numbers F(1) through F(n) and such that n is not a multiple of 24.

1, 2, 77, 319, 323, 1517, 3021, 4757, 6479, 7221, 8159, 8229, 9797, 11663, 12597, 13629, 13869, 14429, 14949, 16637, 18407, 19043, 19437, 23407, 24947, 25437, 30049, 30621, 34943, 34989, 35207, 39203, 43677, 44099, 47519, 51983, 53663, 55221, 65471, 70221, 77837, 78089, 79547

Offset

1,2

Comments

Numbers n which divide the sum of the first n nonzero Fibonacci numbers are listed in A111035 = {1, 2, 24, 48, 72, 77, 96, ...}. Most of these are multiples of 24. These multiples divided by 24 are listed in A124455 = {1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ...}. [Edited by M. F. Hasler, Feb 04 2020]

A111035(2024) = 758642 is in this sequence but not in A331976. - Don Reble, Feb 04 2020

The even terms a({2, 155, 397, 469, ...}) = {2, 758642, 7057466, 10805846, ...} are now listed in A331870. - M. F. Hasler, Feb 06 2020

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 200 terms from M. F. Hasler)

Formula

{ n != 0 (mod 24) | A000071(n+2) == 0 (mod n) }. - M. F. Hasler, Feb 06 2020

Mathematica

Select[Range[20000], !IntegerQ[ #/24]&&Mod[Fibonacci[ #+2]-1, # ]==0&]

Prog

(PARI) A124456_vec(N=44, n=0)={vector(N, i, until( n++%24&& is_A111035(n), ); n)} \\ M. F. Hasler, Feb 04 2020
(Sage) [n for n in (1..20000) if mod(n, 24)!=0 and mod(fibonacci(n+2)-1, n)==0 ] # G. C. Greubel, Feb 16 2020

Crossrefs

Cf. A000045, A111035, A124455.

Cf. A331976 (odd terms).

Sequence in context: A301472 A041721 A048358 * A338588 A364696 A308373

Adjacent sequences: A124453 A124454 A124455 * A124457 A124458 A124459

Keyword

nonn

Author

Alexander Adamchuk, Nov 02 2006, Nov 03 2006

Extensions

Edited by M. F. Hasler, Feb 04 2020

Status

approved