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
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*(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.
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^(2-i)*T[i]: i in [1..#T] ]; [ n: n in [0..1340000] | not IsIrreducible(P+n) ];
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Dec 27 2007
STATUS
approved