A305419 Largest k < n whose binary expansion encodes an irreducible (0,1)-polynomial over GF(2)[X], with a(1) = a(2) = 1.

1, 1, 2, 3, 3, 3, 3, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 13, 13, 19, 19, 19, 19, 19, 19, 25, 25, 25, 25, 25, 25, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 41, 41, 41, 41, 41, 41, 47, 47, 47, 47, 47, 47, 47, 47, 55, 55, 55, 55, 59, 59, 61, 61, 61, 61, 61, 61, 67, 67, 67, 67, 67, 67, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 87

Offset: 1

Author

Antti Karttunen, Jun 07 2018

Keywords

• nonn

Comments

For n >= 3, a(n) is the largest term of A014580 less 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, A305420, A305422.

Cf. also A151799 (A136548), A305429.

Programs

PARI

A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));