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%I #15 Mar 24 2024 07:58:26
%S 2,3,7,13,17,23,37,41,43,47,53,61,67,73,83,89,97,103,107,109,113,127,
%T 137,149,157,163,167,173,193,197,223,227,233,241,257,263,269,277,281,
%U 283,293,307,313,317,337,347,353,367,373,383,389,397,401,409,421,433
%N Primes that yield a simple orbit structure in 2-step recursions.
%C Consider the 2-step recursion x(k)=x(k-1)+x(k-2) mod n. For any of the n^2 initial conditions x(1) and x(2) 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), have the same length.
%C Except for 5, this appears to be the complement of A053032, odd primes p with one 0 in Fibonacci numbers mod p. - _T. D. Noe_, May 03 2005
%C A prime p is in this sequence if either (1) the polynomial x^2-x-1 mod p has no zeros for x in [0,p-1] (see A086937) or (2) the polynomial has zeros, but none is a root of unity mod p. The first few primes in the second category are 41, 61, 89 and 109. - _T. D. Noe_, May 12 2005
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%Y Cf. A015134 (orbits of 2-step sequences).
%K nonn
%O 1,1
%A _T. D. Noe_, May 02 2005