login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A072378 Numbers n such that 12*n divides F(12*n), where F(m) is the m-th 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 (list; graph; refs; listen; history; text; internal format)
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: 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 06:11 EST 2020. Contains 338781 sequences. (Running on oeis4.)