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Search: id:A106300
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| A106300 |
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Primes that do not divide any term of the Lucas 4-step sequence A073817. |
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3
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| 2789, 3847, 4451, 4751, 5431, 6203, 8317, 9533, 9629, 9907, 10093, 11839, 13903, 13907, 14207, 15823, 16319, 16759, 19543, 20939, 21379, 21859, 25303, 26683, 29483, 30871, 31267, 31699, 32003, 32771, 33967, 34963, 36229, 37061, 39983
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If a prime p divides a term a(k) of this sequence, then k must be less than the period of the sequence mod p. Hence these primes are found by computing A073817(k) mod p for increasing k and stopping when either A073817(k) mod p = 0 or the end of the period is reached. Interestingly, for all of these primes, the period of the sequence A073817(k) mod p appears to be (p-1)/d, where d is a small integer.
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LINKS
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Eric Weisstein's World of Mathematics, Fibonacci n-Step
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MATHEMATICA
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n=4; lst={}; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; While[s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; !(a==a0 || s==0)]; If[s>0, AppendTo[lst, p]], {i, 10000}]; lst
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CROSSREFS
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Cf. A053028 (primes not dividing any Lucas number), A106299 (primes not dividing any Lucas 3-step number), A106301 (primes not dividing any Lucas 5-step number).
Sequence in context: A099691 A119377 A014895 this_sequence A115471 A022233 A102170
Adjacent sequences: A106297 A106298 A106299 this_sequence A106301 A106302 A106303
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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
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