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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
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 (list; graph; refs; listen; history; text; internal format)
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 A130807 A338577

Adjacent sequences:  A215639 A215640 A215641 * A215643 A215644 A215645

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Aug 18 2012

STATUS

approved

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Last modified June 18 11:58 EDT 2021. Contains 345098 sequences. (Running on oeis4.)