A305430 Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q.

2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 25, 25, 29, 29, 29, 29, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 55, 55, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67, 67, 69, 69, 71, 71, 73, 73, 77, 77, 77, 77, 79, 79, 81, 81, 83, 83, 87, 87, 87, 87, 89, 89

Offset: 1

Author

Antti Karttunen, Jun 07 2018

Keywords

• nonn

Comments

a(n) is the smallest term of A206074 greater than n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..21845

Crossrefs

Cf. A206074, A257000, A305429.

Cf. also A151800, A305420.

Programs

Mathematica

binPol[n_, x_] := With[{bb = IntegerDigits[n, 2]},bb.x^Range[Length[bb]-1, 0, -1]];
b[n_] := If[IrreduciblePolynomialQ[binPol[n, x]], 1, 0];
a[n_] := Module[{k = n+1}, While[b[k] == 0, k++]; k];
Array[a, 100] (* Jean-François Alcover, Dec 20 2021 *)

PARI

A257000(n) = polisirreducible(Pol(binary(n)));
A305430(n) = { my(k=1+n); while(!A257000(k),k++); (k); };