A255569 Primes whose binary representation encodes an irreducible polynomial over GF(2) and has a nonprime number of 1's.

2, 1019, 1279, 1531, 1663, 1759, 1783, 1789, 2011, 2027, 2543, 2551, 2687, 2879, 2927, 2999, 3037, 3319, 3517, 3547, 3559, 3709, 3833, 3947, 4007, 4013, 4021, 4051, 4073, 4591, 5023, 5039, 5051, 5107, 5563, 5591, 5743, 5821, 5981, 6067, 6271, 6607, 6637, 6779, 6959, 7079, 7351, 7411, 7517, 7541, 7591, 7603, 7727, 7741, 7823, 7907, 7963, 7993

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(n)
  local a, i, x;
  if not isprime(n) then return false fi;
  a:= convert(n, base, 2);
  not isprime(convert(a, `+`)) and (Irreduc(add(x^(i-1)*a[i], i=1..nops(a))) mod 2)
end proc:
select(filter, [2, 2*j+1$j=1..10000]); # Robert Israel, May 14 2015

Mathematica

okQ[p_?PrimeQ] := Module[{id, pol, x}, id = IntegerDigits[p, 2] // Reverse; pol = id.x^Range[0, Length[id]-1]; IrreduciblePolynomialQ[pol, Modulus -> 2] && !PrimeQ[Count[id, 1]]];
Select[Prime[Range[1000]], okQ] (* Jean-François Alcover, Feb 09 2023 *)

Prog

(PARI)
isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
i = 0; forprime(n=2, 2^31, if(isA014580(n)&&!isprime(hammingweight(n)), i++; write("b255569.txt", i, " ", n); if(i>=10000, return(n))));

Crossrefs

Intersection of A091206 and A084345.

Intersection of A014580 and A255564.

Sequence in context: A258661 A370557 A024033 * A354534 A004897 A004802

Adjacent sequences: A255566 A255567 A255568 * A255570 A255571 A255572

Keyword

nonn

Author

Antti Karttunen, May 14 2015 after Joerg Arndt's Nov 01 2013 comment in A091206

Status

approved