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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A301759 Semiperiods of the Fibonacci sequence mod n. 0
1, 3, 4, 6, 10, 12, 8, 12, 12, 30, 10, 24, 14, 24, 40, 24, 18, 12, 18, 60, 16, 30, 24, 24, 50, 42, 36, 48, 14, 120, 30, 48, 40, 18, 80, 24, 38, 18, 56, 60, 20, 48, 44, 30, 120, 24, 16, 24, 56, 150, 72, 84, 54, 36, 20, 48, 72, 42, 58, 120, 30, 30, 48, 96, 70, 120, 68, 36, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is the period of the Fibonacci sequence up to sign.

LINKS

Table of n, a(n) for n=1..69.

Tom Harris, Notes on the Pisano Semiperiod, Dec. 2017.

David Singerman, James Strudwick, Petrie polygons, Fibonacci sequences and Farey maps, Ars Mathematica Contemporanea 10, 2 (2016), 349-357.

David Singerman, James Strudwick, The Farey Maps Modulo N, arXiv:1803.08851 [math.GR], 2018. See p. 6.

EXAMPLE

For n = 7 we get 1,0,1,1,2,3,5,1,-1,0,-1,-1... so a(7) = 8.

PROG

(PARI) a(n) = if (n==1, 1, for(k=1, oo, if (((fibonacci(k) % n) == 0) && (((fibonacci(k+1) % n) == 1) || ((fibonacci(k+1) % n) == n-1)), return (k))));

CROSSREFS

Cf. A000045 (Fibonacci numbers), A001175 (Pisano periods).

Sequence in context: A284528 A176865 A047296 * A322457 A137951 A082694

Adjacent sequences:  A301756 A301757 A301758 * A301760 A301761 A301762

KEYWORD

nonn

AUTHOR

Michel Marcus, Mar 26 2018

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 June 17 05:50 EDT 2021. Contains 345080 sequences. (Running on oeis4.)