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

1,1

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

Table of n, a(n) for n=1..41.

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

Crossrefs

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

Sequence in context: A040119 A186635 A265807 * A036797 A163079 A109845

Adjacent sequences: A106305 A106306 A106307 * A106309 A106310 A106311

Keyword

nonn

Author

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

Status

approved