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

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

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Last modified November 19 03:44 EST 2019. Contains 329310 sequences. (Running on oeis4.)