A124455 Numbers n such that 24n divides the sum of the first 24n nonzero Fibonacci numbers.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 24, 25, 27, 28, 30, 32, 36, 40, 42, 45, 46, 48, 50, 51, 54, 55, 56, 57, 60, 64, 70, 72, 75, 80, 81, 84, 86, 90, 92, 96, 98, 100, 102, 108, 110, 112, 114, 120, 125, 126, 128, 135, 138, 140, 144, 150, 153, 155, 160, 162

Offset: 1

Author

Alexander Adamchuk, Nov 02 2006

Keywords

• nonn

Comments

Numbers n such that n divides the sum of the first n nonzero Fibonacci numbers are listed in A111035 = {1, 2, 24, 48, 72, 77, 96, 120, 144, 192, 216, 240, 288, 319, 323, 336, 360, ...}. Most of these are multiples of 24. Those which are not a multiple of 24 are listed in A124456 = {1, 2, 77, 319, 323, 1517, 3021, 4757, 6479, 7221, 8159, 8229, 9797, ...}.

This sequence coincides with A072378 (12n | F(12n)) for all values up to 84. The first two different terms are 86 and 164.

Prime a(n) are {2, 3, 5, 281, ...}.

Crossrefs

Cf. A111035, A124456, A072378 (numbers n such that 12n divides Fibonacci(12n)), A000045 (Fibonacci numbers).

Programs

Mathematica

Select[Range[10000], IntegerQ[ #/24]&&Mod[Fibonacci[ #+2]-1, # ]==0&] /24

Extensions

Edited by M. F. Hasler, Feb 04 2020