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

1,2

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, ...

Links

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

Example

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

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 *)

Prog

(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, ", ")));

Crossrefs

Cf. A086167, A086168.

Sequence in context: A014634 A303857 A278337 * A126228 A072251 A002756

Adjacent sequences: A270560 A270561 A270562 * A270564 A270565 A270566

Keyword

nonn

Author

Altug Alkan, Mar 19 2016

Extensions

More terms from Amiram Eldar, Jan 03 2020

Status

approved