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

1,1

Comments

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

Links

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

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 *)

Prog

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

Crossrefs

Cf. A206074, A257000, A305429.

Cf. also A151800, A305420.

Sequence in context: A126762 A082048 A113459 * A159477 A268101 A123318

Adjacent sequences: A305427 A305428 A305429 * A305431 A305432 A305433

Keyword

nonn

Author

Antti Karttunen, Jun 07 2018

Status

approved