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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

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Last modified May 25 10:43 EDT 2016. Contains 273288 sequences.