This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A136362 #4 Feb 16 2025 08:33:07 %S A136362 1,2,34,254,898,2302,4898,9214,15874,25598,39202,57598,81794,112894, %T A136362 152098,200702,260098,331774,417314,518398,636802,774398,933154, %U A136362 1115134,1322498 %N A136362 Numbers n such that P+n is not irreducible, where P = x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 2. %C A136362 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. %H A136362 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html">Chebyshev Polynomial of the First Kind</a> %F A136362 a(1) = 1; a(2) = 2; for n > 2, a(n) = 4*n^2*(n-2)^2-2. %F A136362 G.f.: x*(4*x^6 - 21*x^5 + 47*x^4 - 94*x^3 - 34*x^2 + 3*x - 1)/(x - 1)^5. %e A136362 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). %o A136362 (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) ]; %Y A136362 Cf. A126270. %K A136362 nonn %O A136362 1,2 %A A136362 _Klaus Brockhaus_, Dec 27 2007