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Search: id:A106299
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| A106299 |
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Primes that do not divide any term of the Lucas 3-step sequence A001644. |
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+0
6
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| 2, 103, 199, 211, 421, 757, 883, 907, 991, 1021, 1123, 1237, 1543, 1567, 1621, 1699, 1753, 1873, 2113, 2539, 2731, 2797, 2803, 3391, 3433, 3463, 3499, 3613, 3631, 3793, 3853, 3919, 4093, 4591, 4723, 4933, 4951, 4987, 5107, 5179, 5527, 5791, 5839, 6073
(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 A001644(k) mod p for increasing k, and stopping when either A001644(k) mod p = 0 or the end of the period is reached. Interestingly, for all of these primes except 211, the period of the sequence A001644(k) mod p is (p-1)/d, where d is a small integer. The only other exceptional primes less than 1000000 are 23977 and 47093.
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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=3; 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, 1000}]; lst
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CROSSREFS
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Cf. A053028 (primes not dividing any Lucas number), A106300 (primes not dividing any Lucas 4-step number), A106301 (primes not dividing any Lucas 5-step number).
Adjacent sequences: A106296 A106297 A106298 this_sequence A106300 A106301 A106302
Sequence in context: A113575 A111012 A055693 this_sequence A101530 A001184 A098653
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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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