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%I #8 Nov 05 2020 14:27:58
%S 7,11,19,29,41,43,53,59,89,109,139,179,181,229,379,401,421,431,541,
%T 587,659,811,991,1069,1103,1117,1231,1259,1459,1471,1619,1709,1831,
%U 1951,2179,2791,2797,2833,2851,3001,3391,3571,3617,3631,3637,3671,3793,3863,3929,3967
%N Odd primes p with (p^2 - 1)/4 - prime((p - 1)/2) and (p^2 - 1)/4 - prime((p + 1)/2) both prime.
%C By the conjecture in A235805, this sequence should have infinitely many terms.
%H Zhi-Wei Sun, <a href="/A235806/b235806.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 7 since neither (3^2-1)/4 - prime((3-1)/2) = 0 nor (5^2-1)/4 - prime((5+1)/2) = 1 is prime, but (7^2-1)/4 - prime((7-1)/2) = 12 - 5 = 7 and (7^2-1)/4 - prime((7+1)/2) = 12 - 7 = 5 are both prime.
%t q[n_]:=PrimeQ[n(n+1)-Prime[n]]&&PrimeQ[n(n+1)-Prime[n+1]]
%t n=0;Do[If[q[(Prime[k]-1)/2],n=n+1;Print[n," ",Prime[k]]],{k,2,1000}]
%t Select[Prime[Range[2,600]],AllTrue[(#^2-1)/4-{Prime[(#-1)/2],Prime[ (#+1)/2]},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 05 2020 *)
%Y Cf. A000040, A235592, A235727, A235805.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jan 16 2014
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