

A106308


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Consider the 4step recursion x(k)=x(k1)+x(k2)+x(k3)+x(k4) 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 nStep


CROSSREFS

Cf. A106286 (orbits of 4step 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



