

A270563


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


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, ); p2}
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



