OFFSET
1,2
COMMENTS
Odd integers n such that n divides the n-th Fibonacci number form sequence A129066, while even such n's are multiples of 12.
a(n) seems to be asymptotic to a constant multiple of n^phi, where phi is the golden ratio.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
D. Shtefan and I. Dobrovolska, The sums of the consecutive Fibonacci numbers,, Fibonacci Quarterly, 56 (2018), 229-236.
EXAMPLE
3 belongs to the sequence because 3*12=36 divides F(36) = 14930352. For every n, 5^n belongs to the sequence, as can be proved by induction.
MATHEMATICA
Select[Range[n], Mod[Fibonacci[12# ], 12# ]==0&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar Antolin Camarena (omar(AT)tlahui.posgrado.unam.mx), Jul 19 2002
EXTENSIONS
Edited by Max Alekseyev, Jan 21 2010
STATUS
approved