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A255569 Primes whose binary representation encodes an irreducible polynomial over GF(2) and has a nonprime number of 1's. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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: A214543 A258661 A024033 * A004897 A004802 A294279

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

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Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)