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

%I A091207 #16 Feb 08 2023 17:38:03
%S A091207 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,
%T A091207 52,53,61,65,75,78,81,84,90,93,95,102,103,107,110,111,112,113,115,118,
%U A091207 121,123,126,128,134,135,136,138,144,149,151,153,156,158,162,163,164
%N A091207 Indices of primes that are also irreducible GF(2)[X]-polynomials.
%H A091207 Robert Israel, <a href="/A091207/b091207.txt">Table of n, a(n) for n = 1..10000</a>
%H A091207 Antti Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence</a>.
%F A091207 a(n) = A049084(A091206(n)).
%p A091207 filter:= proc(p) local L,i,x;
%p A091207   L:= convert(p,base,2);
%p A091207   Irreduc(add(L[i]*x^(i-1),i=1..nops(L))) mod 2
%p A091207 end proc:
%p A091207 select(t -> filter(ithprime(t)), [$1..300]); # _Robert Israel_, Jun 12 2018
%t A091207 okQ[p_] := PrimeQ[p] && Module[{id, pol}, id = IntegerDigits[p, 2] // Reverse; pol = id.x^Range[0, Length[id] - 1]; IrreduciblePolynomialQ[pol, Modulus -> 2]];
%t A091207 Select[Range[300], okQ[Prime[#]]&] (* _Jean-François Alcover_, Feb 07 2023 *)
%o A091207 (PARI) isok(n) = polisirreducible(Mod(1, 2)*Pol(binary(prime(n)))); \\ _Michel Marcus_, Jun 13 2018
%Y A091207 Cf. A049084, A091206.
%Y A091207 Complement of A091210.
%K A091207 nonn
%O A091207 1,2
%A A091207 _Antti Karttunen_, Jan 03 2004