A305420 Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X].

2, 3, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 19, 19, 19, 19, 19, 19, 25, 25, 25, 25, 25, 25, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 47, 47, 47, 47, 47, 47, 55, 55, 55, 55, 55, 55, 55, 55, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67, 67, 73, 73, 73, 73, 73, 73, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 87, 91

Offset: 1

Author

Antti Karttunen, Jun 07 2018

Keywords

• nonn

Comments

a(n) is the smallest term of A014580 greater than n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..21845
• Index entries for sequences related to polynomials in ring GF(2)[X]

Crossrefs

Cf. A014580, A091225, A091228, A305419, A305421.

Cf. also A151800, A305430.

Programs

PARI

A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
A305420(n) = { my(k=1+n); while(!A091225(k),k++); (k); };

Formula

For n >= 1, a(n) = A091228(1+n).