

A072378


Numbers n such that 12n divides F(12n) 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.


REFERENCES

D. Shtefan and I. Dobrovolska, The sums of the consecutive Fibonacci numbers, Fib. Q., 56 (2018), 229236.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000


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.
Sequence in context: A295585 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



