login
Primes p such that the least k with p+k and p+2k both prime sets a new record.
2

%I #9 Oct 12 2021 13:30:41

%S 3,5,13,37,73,179,503,757,1223,1249,1831,2003,4051,6991,17483,18353,

%T 18457,22567,26993,47129,88327,131357,136753,215753,344293,499673,

%U 2499143,3345877,3984391,4065461,5062649,5418421,7933109,8865331,11339287,12464401,18606089

%N Primes p such that the least k with p+k and p+2k both prime sets a new record.

%C This sequence is conjectured to be infinite, but this is expected to be roughly as hard as the twin prime conjecture.

%H Donovan Johnson, <a href="/A190423/b190423.txt">Table of n, a(n) for n = 1..60</a>

%o (PARI) print1(r=3); forprime(p=5, 4e9, forstep(k=6,9e9, 6, if(isprime(p+k) && isprime(p+2*k), if(k>r, r=k; print1(", "p)); break)))

%Y Cf. A120627, A190424.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, May 10 2011