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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.

%I A215642 #20 Aug 20 2012 13:49:46
%S A215642 2,3,5,7,11,13,19,23,31,37,41,43,47,53,59,61,73,79,83,103,107,109,113,
%T A215642 127,137,139,149,151,157,179,181,199,223,227,229,239,251,271,277,281,
%U A215642 293,311,331,349,353,359,367,379,383,389,397,401,409,421,431,439,487,499,541
%N A215642 Primes p such that there is no D such that p+D, p-D, p+2*D, p-2*D are all primes.
%C A215642 Conjecture: a(243)=34613 is the last term.
%H A215642 Joerg Arndt, <a href="/A215642/b215642.txt">Table of n, a(n) for n = 1..243</a>
%e A215642 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.
%t A215642 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 *)
%o A215642 (PARI)
%o A215642 N=10^9;
%o A215642 default(primelimit,N);
%o A215642 print1(2,", ");
%o A215642 { forprime (p=3, N,
%o A215642     D=2;  D2 = D << 1;
%o A215642     t = 1;
%o A215642     while ( p > D2,
%o A215642         if ( isprime(p+D) & isprime(p-D) &
%o A215642              isprime(p+D2) & isprime(p-D2)
%o A215642         , /* then */
%o A215642             t=0; break()
%o A215642         );
%o A215642         D += 2;  D2 += 4;
%o A215642     );
%o A215642     if ( t==1, print1(p,", ") );
%o A215642 ); }
%o A215642 /* _Joerg Arndt_, Aug 20 2012 */
%Y A215642 Cf. A078611.
%K A215642 nonn
%O A215642 1,1
%A A215642 _Alex Ratushnyak_, Aug 18 2012