

A136362


Numbers n such that P+n is not irreducible, where P = x^8  8*x^6 + 20*x^4  16*x^2 + 2.


1



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
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OFFSET

1,2


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..25.
Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind


FORMULA

a(1) = 1; a(2) = 2; for n > 2, a(n) = 4*n^2*(n2)^22.
G.f.: x*(4*x^6  21*x^5 + 47*x^4  94*x^3  34*x^2 + 3*x  1)/(x  1)^5.


EXAMPLE

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).


PROG

(MAGMA) Zx<x>:= PolynomialRing(Integers()); T:=Coefficients(ChebyshevT(8)); P:=Zx ! [ 2^(2i)*T[i]: i in [1..#T] ]; [ n: n in [0..1340000]  not IsIrreducible(P+n) ];


CROSSREFS

Cf. A126270.
Sequence in context: A131471 A318268 A036827 * A220507 A263689 A098531
Adjacent sequences: A136359 A136360 A136361 * A136363 A136364 A136365


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Dec 27 2007


STATUS

approved



