A270563 - OEIS

%I #18 Jan 03 2020 10:31:50

%S 1,15,45,105,135,231,807,1215,1329,1395,1593,1911,2301,2331,2493,3045,

%T 3267,3417,3495,3897,4029,4059,4359,4377,4635,4665,4731,5265,6135,

%U 6315,6429,6489,6795,6915,6999,7329,7515,7965,8469,8979,9183,9441,10755,11193,12039

%N Integers k such that A086167(k) and A086168(k) are both prime.

%C A013916 lists numbers n such that the sum of the first n primes is prime. With similar motivation, twin prime pairs generate prime pairs in this sequence. Note that 2*n also gives the difference between members of prime pair that is generated by sum of first n twin prime pairs.

%C First differences of this sequence are 14, 30, 60, 30, 96, 576, ...

%H Amiram Eldar, <a href="/A270563/b270563.txt">Table of n, a(n) for n = 1..10000</a>

%e 15 is a term since A086167(15) = 1297 and A086168(15) = 1297 + 15*2 = 1327. 1297 and 1327 are both prime.

%t seq = {}; s1 = s2 = 0; c = n = 0; p = prv = 2; While[c < 45, p = NextPrime[p]; If[p == prv + 2, n++; s1 += prv; s2 += p; If[PrimeQ[s1] && PrimeQ[s2], c++; AppendTo[seq, n]]]; prv = p]; seq (* _Amiram Eldar_, Jan 03 2020 *)

%o (PARI) t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}

%o s1(n) = sum(k=1, n, t(k));

%o s2(n) = sum(k=1, n, t(k)+2);

%o for(n=1, 1e3, if(ispseudoprime(s1(n)) && ispseudoprime(s2(n)), print1(n, ", ")));

%Y Cf. A086167, A086168.

%K nonn

%O 1,2

%A _Altug Alkan_, Mar 19 2016

%E More terms from _Amiram Eldar_, Jan 03 2020