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A305430
Smallest k > n whose binary expansion encodes an irreducible (0,1)-polynomial over Q.
4
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
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. also A151800, A305420.
Sequence in context: A126762 A082048 A113459 * A159477 A268101 A123318
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 07 2018
STATUS
approved