A091207 Indices of primes that are also irreducible GF(2)[X]-polynomials.

1, 2, 4, 5, 6, 8, 11, 12, 13, 15, 17, 18, 19, 21, 25, 27, 29, 32, 33, 37, 39, 43, 44, 47, 50, 52, 53, 61, 65, 75, 78, 81, 84, 90, 93, 95, 102, 103, 107, 110, 111, 112, 113, 115, 118, 121, 123, 126, 128, 134, 135, 136, 138, 144, 149, 151, 153, 156, 158, 162, 163, 164

Offset: 1

Author

Antti Karttunen, Jan 03 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Antti Karttunen, Scheme-program for computing this sequence.

Crossrefs

Cf. A049084, A091206.

Complement of A091210.

Programs

Maple

filter:= proc(p) local L,i,x;
  L:= convert(p,base,2);
  Irreduc(add(L[i]*x^(i-1),i=1..nops(L))) mod 2
end proc:
select(t -> filter(ithprime(t)), [$1..300]); # Robert Israel, Jun 12 2018

Mathematica

okQ[p_] := PrimeQ[p] && Module[{id, pol}, id = IntegerDigits[p, 2] // Reverse; pol = id.x^Range[0, Length[id] - 1]; IrreduciblePolynomialQ[pol, Modulus -> 2]];
Select[Range[300], okQ[Prime[#]]&] (* Jean-François Alcover, Feb 07 2023 *)

PARI

isok(n) = polisirreducible(Mod(1, 2)*Pol(binary(prime(n)))); \\ Michel Marcus, Jun 13 2018

Formula

a(n) = A049084(A091206(n)).