login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060305 Related to Pisano periods: period of Fibonacci numbers mod prime(n). 9
3, 8, 20, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178, 90, 190, 388, 396, 22, 42, 448, 456, 114, 52, 238, 240, 250, 516, 176, 268, 270, 556 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Assuming Wall's conjecture (which is still open) allows one to calculate A001175(m) when m is a prime power since for any k>=1 : A001175(prime(n)^k)=a(n)*prime(n)^(k-1). For example : A001175(2^k)=3*2^(k-1)=A007283(k-1)

LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014.

A. Elsenhans, J. Jahnel, The Fibonacci sequence modulo p^2 -- An investigation by computer for p < 10^14, (2004)

D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.

MAPLE

a:= proc(n) option remember; local F, k, p;

      F:=[1, 1]; p:=ithprime(n);

      for k while F<>[0, 1] do

        F:=[F[2], irem(F[1]+F[2], p)]

      od: k

    end:

seq(a(n), n=1..70);  # Alois P. Heinz, Oct 16 2015

MATHEMATICA

Table[p=Prime[n]; a={1, 0}; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[2]]=s; a!=a0]; k, {n, 100}] (* T. D. Noe, Jun 12 2006 *)

PROG

(PARI) for(n=1, 100, s=1; while(sum(i=n, n+s, abs(fibonacci(i)%prime(n)-fibonacci(i+s)%prime(n)))+sum(i=n+1, n+1+s, abs(fibonacci(i)%prime(n)-fibonacci(i+s)%prime(n)))>0, s++); print1(s, ", "))

CROSSREFS

Cf. A001175, A000961, A071774, A003147.

Sequence in context: A170900 A151347 A047093 * A009141 A090069 A272528

Adjacent sequences:  A060302 A060303 A060304 * A060306 A060307 A060308

KEYWORD

nonn

AUTHOR

Louis Mello (mellols(AT)aol.com), Mar 26 2001

EXTENSIONS

Corrected by Benoit Cloitre, Jun 04 2002

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 21:23 EST 2016. Contains 279011 sequences.