%I #10 Feb 10 2020 22:55:52

%S 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,

%T 46,48,50,51,54,55,56,57,60,64,70,72,75,80,81,84,86,90,92,96,98,100,

%U 102,108,110,112,114,120,125,126,128,135,138,140,144,150,153,155,160,162

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

%C 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, ...}.

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

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

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

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

%K nonn

%O 1,2

%A _Alexander Adamchuk_, Nov 02 2006

%E Edited by _M. F. Hasler_, Feb 04 2020