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%I #12 Dec 14 2014 23:26:07
%S 140611,1000003,68921003,81746507,105154051,360944131,709732291,
%T 1643032003,8072216219,8390176771,10021812419,10823192131,11239424003,
%U 14526784003,15363967259,17014253251,23689358851,24693014531,26784575491,27270901003,27928443307,36594368003
%N Primes of the form (p + q)^3 + 3, where p and q are consecutive primes.
%H K. D. Bajpai, <a href="/A252017/b252017.txt">Table of n, a(n) for n = 1..12289</a>
%e 140611 is in the sequence because (23 + 29)^3 + 3 = 140611 which is prime: 23 and 29 are consecutive primes.
%e 81746507 is in the sequence because (211 + 223)^3 + 3 = 81746507 which is prime: 211 and 223 are consecutive primes.
%t Select[Table[(Prime[n] + Prime[n + 1])^3 + 3, {n, 500}], PrimeQ[#] &]
%o (PARI) s=[]; for(k=1, 500, t=(prime(k) + prime(k+1))^3 + 3; if(isprime(t), s=concat(s, t))); s
%Y Cf. A000040, A007645, A003136, A243761.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Dec 13 2014