

A072378


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


7



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
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OFFSET

1,2


COMMENTS

Odd integers n such that n divides the nth 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), 229236.


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: A324578 A193988 A124455 * A248888 A112587 A141820
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



