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, 2, 34, 254, 898, 2302, 4898, 9214, 15874, 25598, 39202, 57598, 81794, 112894, 152098, 200702, 260098, 331774, 417314, 518398, 636802, 774398, 933154, 1115134, 1322498

Offset: 1

Author

Klaus Brockhaus, Dec 27 2007

Keywords

• nonn

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.

Examples

			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).
		

Links

• Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind

Crossrefs

Cf. A126270.

Programs

Magma

Zx:= 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) ];

Formula

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.