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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A106307 Primes that yield a simple orbit structure in 3-step recursions.

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%I A106307 #11 Feb 16 2025 08:32:57
%S A106307 3,5,23,31,37,59,67,71,89,97,103,113,137,157,179,181,191,223,229,251,
%T A106307 313,317,331,353,367,379,383,389,433,443,449,463,467,487,509,521,577,
%U A106307 587,619,631,641,643,647,653,661,691,709,719,727,751,797,823,829
%N A106307 Primes that yield a simple orbit structure in 3-step recursions.
%C A106307 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.
%C A106307 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.
%H A106307 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>.
%Y A106307 Cf. A106285 (orbits of 3-step sequences).
%K A106307 nonn
%O A106307 1,1
%A A106307 _T. D. Noe_, May 02 2005, revised May 12 2005