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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, ); 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

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Last modified November 26 17:17 EST 2020. Contains 338641 sequences. (Running on oeis4.)