A270563 Integers k such that A086167(k) and A086168(k) are both prime.

1, 15, 45, 105, 135, 231, 807, 1215, 1329, 1395, 1593, 1911, 2301, 2331, 2493, 3045, 3267, 3417, 3495, 3897, 4029, 4059, 4359, 4377, 4635, 4665, 4731, 5265, 6135, 6315, 6429, 6489, 6795, 6915, 6999, 7329, 7515, 7965, 8469, 8979, 9183, 9441, 10755, 11193, 12039

Offset: 1

Author

Altug Alkan, Mar 19 2016

Keywords

• nonn

Comments

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.

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A086167, A086168.

Programs

Mathematica

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 *)

PARI

t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}
s1(n) = sum(k=1, n, t(k));
s2(n) = sum(k=1, n, t(k)+2);
for(n=1, 1e3, if(ispseudoprime(s1(n)) && ispseudoprime(s2(n)), print1(n, ", ")));

Extensions

More terms from Amiram Eldar, Jan 03 2020