A305821 a(n) = 1 if n is composite and its binary expansion encodes an irreducible (0,1)-polynomial when factored over Q, 0 otherwise.

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

Offset

1

Comments

Characteristic function for A206075, apart from its initial term.

Links

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

Index entries for characteristic functions

Formula

a(n) = A257000(n) - A010051(n).

Example

For n = 25 we know that it is composite as 25 = 5*5, but nevertheless, its binary representation "11001" encodes a (0,1)-polynomial x^4 + x^3 + 1, which is irreducible when factored over Q, thus a(25) = 1.

Prog

(PARI) A305821(n) = (!isprime(n) && polisirreducible(Pol(binary(n))));

Crossrefs

Cf. A010051, A257000, A206075, A305790.

Sequence in context: A085974 A011739 A023975 * A305892 A324870 A011738

Adjacent sequences: A305818 A305819 A305820 * A305822 A305823 A305824

Keyword

nonn

Author

Antti Karttunen, Jun 10 2018

Status

approved