Positive integers n such that the polynomial P(n,t) = t^{2^{n-1}} * (t+1)^{2^{n-1}-1} + 1 of GF(2)[t] is irreducible, where GF(2) = {0,1} is the binary finite field with two elements.

For n=1 the polynomial P(1,t)=t+1 is irreducible in GF(2)[t]. For n=3 the polynomial P(3,t)=t^4(t+1)^3+1 = t^7+t^6+t^5+t^4+1 is irreducible in GF(2)[t].

PROG

(PARI) isok(n) = polisirreducible(Mod(1, 2)*(t^(2^(n-1))*(t+1)^(2^(n-1)-1)+1)); \\ Michel Marcus, Aug 14 2013