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