A305816 a(n) = 1 if n is a prime whose binary expansion encodes a (0,1)-polynomial which is irreducible when factored over GF(2), 0 otherwise.

0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0

Offset

1

Comments

Characteristic function of A091206.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences operating on GF(2)[X]-polynomials

Formula

a(n) = A010051(n)*A091225(n).

a(n) = [A305789(n) == 2].

Prog

(PARI) A305816(n) = (isprime(n)&&polisirreducible(Pol(binary(n))*Mod(1, 2)));

Crossrefs

Cf. A091206, A305802, A305789, A305817 (partial sums), A305904.

Sequence in context: A284901 A071981 A280910 * A359820 A241979 A200244

Adjacent sequences: A305813 A305814 A305815 * A305817 A305818 A305819

Keyword

nonn

Author

Antti Karttunen, Jun 15 2018

Status

approved