A162570 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.

1, 2, 3, 4, 6, 7, 15

Offset

1,2

Links

Table of n, a(n) for n=1..7.

Example

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

Crossrefs

Sequence in context: A096477 A039059 A151892 * A073639 A130776 A077292

Adjacent sequences: A162567 A162568 A162569 * A162571 A162572 A162573

Keyword

nonn,hard,more

Author

Luis H. Gallardo, Jul 06 2009

Status

approved