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

Author

Omar Antolin Camarena (omar(AT)tlahui.posgrado.unam.mx), Jul 19 2002

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A128974, A317971.

Programs

Mathematica

Select[Range[n], Mod[Fibonacci[12# ], 12# ]==0&]

Extensions

Edited by Max Alekseyev, Jan 21 2010