1,2

Also, number of perfect multi-Skolem type sequences of order n.

Index the Fibonacci numbers so that 3 is the fourth number. If the modulo base is a Fibonacci number (>=3) with an even index, the period is twice the index. If the base is a Fibonacci number (>=5) with an odd index, the period is 4 times the index. - Kerry Mitchell (lkmitch(AT)gmail.com), Dec 11 2005

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Crux Mathematicorum, Fibonacci Residues, 1997 Vol. 23 No. 4 pp. 224-6 CMS

J. D. Fulton and W. L. Morris, On arithmetical functions related to the Fibonacci numbers, Acta Arithmetica, 16 (1969), 105-110.

B. H. Hannon and W. L. Morris, Tables of Arithmetical Functions Related to the Fibonacci Numbers. Report ORNL-4261, Oak Ridge National Laboratory, Oak Ridge, Tennessee, Jun 1968.

Review of B. H. Hannon and W. L. Morris tables, Math. Comp., 23 (1969), 459-460.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 162.

D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly (67 #6, Jun-Jul 1960), pp. 525-532.

T. D. Noe, Table of n, a(n) for n = 1..10000

K. S. Brown, Periods of Fibonacci Sequences mod m

D. A. Coleman et al., Periods of (q,r)-Fibonacci sequences and Elliptic Curves, Fibonacci Quart. 44, no 1 (2006) 59-70.

G. Nordh, Perfect Skolem sequences

N. Patson, Pisano period and permutations of n X n matrices, Australian Math. Soc. Gazette, 2007.

M. Renault, Periods of Fibonacci Sequence Modulo m

Eric Weisstein's World of Mathematics, Pisano Number

Let the prime factorization of n be p1^e1...pk^ek. Then a(n) = lcm(a(p1^e1), ..., a(pk^ek)). - T. D. Noe (noe(AT)sspectra.com), May 02 2005

a(n) = n-1 if n is a prime > 5 included in A003147 ( n = 11, 19, 31, 41, 59, 61, 71, 79, 109...) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2002

K. S. Brown shows that a(n)/n <= 6 for all n and a(n)=6n if and only if n has the form 2*5^k.

a(n) = A001177(n)*A001176(n) for n >= 1. - Henry Bottomley (se16(AT)btinternet.com), Dec 19 2001

Table[a={1, 0}; a0=a; k=0; While[k++; s=Mod[Plus@@a, n]; a=RotateLeft[a]; a[[2]]=s; a!=a0]; k, {n, 2, 100}] (Noe)

Cf. A060305 (Fibonacci period mod prime(n)).

Sequence in context: A098737 A164654 A072396 this_sequence A093725 A011413 A010629

Adjacent sequences: A001172 A001173 A001174 this_sequence A001176 A001177 A001178

nonn,nice

N. J. A. Sloane (njas(AT)research.att.com).