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Search: id:A087612
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| A087612 |
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A divisibility sequence derived from Lehmer's polynomial x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1. Square root of the terms in A059928. |
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3
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| 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 13, 29, 3, 1, 1, 37, 3, 1, 23, 1, 9, 49, 25, 1, 39, 1, 29, 32, 93, 67, 1, 71, 27, 1, 37, 79, 3, 83, 13, 173, 69, 29, 47, 1, 423, 293, 49, 103, 75, 317, 53, 109, 39, 37, 59, 1297, 261, 367, 1024, 1, 93, 1, 1541, 269, 201, 277, 923, 283, 1917
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The sequence is conjectured to contain an infinite number of primes. The first 100 terms contain 33 unique primes. As stated by Everest and Ward, except for a finite number of composite n, a(n) can be prime only if n is prime. For this sequence, n=23*47 is the largest composite for which a(n) is prime.
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REFERENCES
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See A059928
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LINKS
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G. Everest and T. Ward, Primes in Divisibility Sequences
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MATHEMATICA
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CompanionMatrix[p_, x_] := Module[{cl=CoefficientList[p, x], deg, m}, cl=Drop[cl/Last[cl], -1]; deg=Length[cl]; If[deg==1, {-cl}, m=RotateLeft[IdentityMatrix[deg]]; m[[ -1]]=-cl; Transpose[m]]]; c=CompanionMatrix[x^10+x^9-x^7-x^6-x^5-x^4-x^3+x+1, x]; im=IdentityMatrix[10]; tmp=im; Table[tmp=tmp.c; Sqrt[Abs[Det[tmp-im]]], {n, 100}]
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CROSSREFS
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Cf. A059928.
Sequence in context: A069292 A091842 A060901 this_sequence A155828 A051997 A155744
Adjacent sequences: A087609 A087610 A087611 this_sequence A087613 A087614 A087615
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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), Sep 15 2003
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