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Search: id:A106308
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| A106308 |
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Primes that yield a simple orbit structure in 4-step recursions. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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Eric Weisstein's World of Mathematics, Fibonacci n-Step
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CROSSREFS
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Cf. A106286 (orbits of 4-step sequences).
Sequence in context: A090475 A060301 A040119 this_sequence A036797 A136611 A109845
Adjacent sequences: A106305 A106306 A106307 this_sequence A106309 A106310 A106311
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 02 2005, revised May 12 2005
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