A309354 - OEIS

%I #19 Aug 01 2019 20:32:35

%S 23,31,41,59,131,211,311,941,1049,1381,1931,2579,3271,3911,4289,4451,

%T 4999,6421,6719,8059,8069,9769,10391,10399,10589,11551,12011,14369,

%U 16249,20479,23269,23629,26591,27031,28309,31379,33349,33521,35339,35491,39019,41081

%N Primes of the form p+q+r where p < q < r = p+6 are consecutive primes.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>

%e P = 5 (prime),

%e P + 2 = 7 (prime),

%e P + 6 = 11 (prime),

%e and 5 + 7 + 11 = 23 is prime and is a term.

%e P = 7 (prime),

%e P + 4 = 11 (prime),

%e P + 6 = 13 (prime)

%e and 7 + 11 + 13 = 31 is prime and is a term.

%e However, (p,q,r) = (13,17,19) fails because the sum is not a prime.

%t Select[Total /@ Select[Partition[Prime@Range[2000], 3, 1], #[[3]] == 6 + #[[1]] &], PrimeQ] (* _Giovanni Resta_, Jul 25 2019 *)

%Y Cf. A098420.

%K nonn

%O 1,1

%A _Philip Mizzi_, Jul 25 2019

%E More terms from _Giovanni Resta_, Jul 25 2019