A072378 Numbers n such that 12*n divides F(12*n), where F(m) is the m-th Fibonacci number.

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, 90, 92, 96, 98, 100, 102, 108, 110, 112, 114, 120, 125, 126, 128, 135, 138, 140, 144, 150, 153, 155, 160, 162, 165

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

Cf. A128974, A317971.

Sequence in context: A373847 A193988 A124455 * A248888 A112587 A372916

Adjacent sequences: A072375 A072376 A072377 * A072379 A072380 A072381

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