This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060305 Pisano periods for primes: period of Fibonacci numbers mod prime(n). 11
 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 and J. Int. Seq. 17 (2014), # 14.8.5. 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. Wikipedia, Pisano period. FORMULA a(n) = A001175(prime(n)). - Jonathan Sondow, Dec 09 2017 a(n) = (3 - L(p))/2 * (p - L(p)) / A296240(n) for n >= 4, where p = prime(n) and L(p) = Legendre(p|5); so a(n) <= p-1 if p == +- 1 mod 5, and a(n) <= 2*p+2 if p == +- 2 mod 5. See Wall's Theorems 6 and 7. - Jonathan Sondow, Dec 10 2017 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, A296240. Sequence in context: A151347 A047093 A304256 * 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 Name clarified by Jonathan Sondow, Dec 09 2017 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.

Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)