A106308 Primes that yield a simple orbit structure in 4-step recursions.

2, 3, 5, 31, 43, 53, 79, 83, 89, 97, 109, 131, 137, 139, 151, 199, 229, 233, 239, 257, 283, 313, 317, 359, 367, 389, 433, 443, 479, 487, 569, 571, 577, 601, 617, 641, 643, 659, 673, 677, 769

Offset: 1

Author

T. D. Noe, May 02 2005, revised May 12 2005

Keywords

• nonn

Comments

Consider the 4-step recursion x(k) = (x(k-1) + x(k-2) + x(k-3) + x(k-4)) mod n. For any of the n^4 initial conditions x(1), x(2), x(3) and x(4) in Zn, the recursion has a finite period. When n is a prime in this sequence, all of the orbits, except the one containing (0,0,0,0), have the same length.

For the prime 3 the orbit structure contains three orbits of length 1: (0,0,0,0), (1,1,1,1) and (2,2,2,2).

Links

• Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.

Crossrefs

Cf. A106286 (orbits of 4-step sequences).