OFFSET
1,1
COMMENTS
Consider the 3-step recursion x(k)=x(k-1)+x(k-2)+x(k-3) mod n. For any of the n^3 initial conditions x(1), x(2) and x(3) in Zn, the recursion has a finite period. When n is a prime in this sequence, all of the orbits, except the one containing (0,0,0), have the same length.
A prime p is in this sequence if either (1) the polynomial x^3-x^2-x-1 mod p has no zeros for x in [0,p-1] (see A106282) or (2) the polynomial has zeros, but none is a root of unity mod p. The first two primes in the second category are 103 and 587.
LINKS
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, May 02 2005, revised May 12 2005
STATUS
approved