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A124456
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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.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 200 terms from M. F. Hasler)
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FORMULA
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{ n != 0 (mod 24) | A000071(n+2) == 0 (mod n) }. - M. F. Hasler, Feb 06 2020
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MATHEMATICA
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Select[Range[20000], !IntegerQ[ #/24]&&Mod[Fibonacci[ #+2]-1, # ]==0&]
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PROG
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(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
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CROSSREFS
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Cf. A000045, A111035, A124455.
Cf. A331976 (odd terms).
Sequence in context: A301472 A041721 A048358 * A338588 A308373 A183578
Adjacent sequences: A124453 A124454 A124455 * A124457 A124458 A124459
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk, Nov 02 2006, Nov 03 2006
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EXTENSIONS
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Edited by M. F. Hasler, Feb 04 2020
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STATUS
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approved
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