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Search: id:A136362
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| A136362 |
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Numbers n such that P+n is not irreducible, where P = x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 2. |
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+0
2
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| 1, 2, 34, 254, 898, 2302, 4898, 9214, 15874, 25598, 39202, 57598, 81794, 112894, 152098, 200702, 260098, 331774, 417314, 518398, 636802, 774398, 933154, 1115134, 1322498
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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P = 2*(substitution of x by x/2 in T_8(x)), where T_8(x) is degree 8 Chebyshev polynomial of the first kind.
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LINKS
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Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind
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FORMULA
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a(1) = 1; a(2) = 2; for n > 2, a(n) = 4*n^2*(n-2)^2-2.
G.f.: x*(4*x^6 - 21*x^5 + 47*x^4 - 94*x^3 - 34*x^2 + 3*x - 1)/(x - 1)^5.
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EXAMPLE
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P+254 = x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 256 = (x^4 - 10*x^2 + 32)*(x^4 + 2*x^2 + 8).
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PROGRAM
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(MAGMA) Zx<x>:= PolynomialRing(Integers()); T:=Coefficients(ChebyshevT(8)); P:=Zx ! [ 2^(2-i)*T[i]: i in [1..#T] ]; [ n: n in [0..1340000] | not IsIrreducible(P+n) ];
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CROSSREFS
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Cf. A126270.
Adjacent sequences: A136359 A136360 A136361 this_sequence A136363 A136364 A136365
Sequence in context: A064202 A131471 A036827 this_sequence A098531 A092408 A005261
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 27 2007
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