A215642 Primes p such that there is no D such that p+D, p-D, p+2*D, p-2*D are all primes.

2, 3, 5, 7, 11, 13, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 73, 79, 83, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 179, 181, 199, 223, 227, 229, 239, 251, 271, 277, 281, 293, 311, 331, 349, 353, 359, 367, 379, 383, 389, 397, 401, 409, 421, 431, 439, 487, 499, 541

Offset

1,1

Comments

Conjecture: a(243)=34613 is the last term.

Links

Joerg Arndt, Table of n, a(n) for n = 1..243

Example

17 doesn't occur in the sequence, because there is D=6: 17-12, 17-6, 17+6 and 17+12 are all primes: 5, 11, 23, 29.

Mathematica

fQ[p_] := Module[{d = 1}, While[4d < p && !(PrimeQ[p-4d] && PrimeQ[p-2d] && PrimeQ[p+2d] && PrimeQ[p+4d]), d++]; 4d > p]; Select[Prime[Range[4000]], fQ] (* T. D. Noe, Aug 20 2012 *)

Prog

(PARI)
N=10^9;
default(primelimit, N);
print1(2, ", ");
{ forprime (p=3, N,
    D=2;  D2 = D << 1;
    t = 1;
    while ( p > D2,
        if ( isprime(p+D) & isprime(p-D) &
             isprime(p+D2) & isprime(p-D2)
        , /* then */
            t=0; break()
        );
        D += 2;  D2 += 4;
    );
    if ( t==1, print1(p, ", ") );
); }
/* Joerg Arndt, Aug 20 2012 */

Crossrefs

Cf. A078611.

Sequence in context: A232824 A078334 A108696 * A092581 A362527 A130807

Adjacent sequences: A215639 A215640 A215641 * A215643 A215644 A215645

Keyword

nonn

Author

Alex Ratushnyak, Aug 18 2012

Status

approved