This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309354 #20 Feb 16 2025 08:33:55 %S A309354 23,31,41,59,131,211,311,941,1049,1381,1931,2579,3271,3911,4289,4451, %T A309354 4999,6421,6719,8059,8069,9769,10391,10399,10589,11551,12011,14369, %U A309354 16249,20479,23269,23629,26591,27031,28309,31379,33349,33521,35339,35491,39019,41081 %N A309354 Primes of the form p+q+r where p < q < r = p+6 are consecutive primes. %H A309354 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a> %e A309354 P = 5 (prime), %e A309354 P + 2 = 7 (prime), %e A309354 P + 6 = 11 (prime), %e A309354 and 5 + 7 + 11 = 23 is prime and is a term. %e A309354 P = 7 (prime), %e A309354 P + 4 = 11 (prime), %e A309354 P + 6 = 13 (prime) %e A309354 and 7 + 11 + 13 = 31 is prime and is a term. %e A309354 However, (p,q,r) = (13,17,19) fails because the sum is not a prime. %t A309354 Select[Total /@ Select[Partition[Prime@Range[2000], 3, 1], #[[3]] == 6 + #[[1]] &], PrimeQ] (* _Giovanni Resta_, Jul 25 2019 *) %Y A309354 Cf. A098420. %K A309354 nonn %O A309354 1,1 %A A309354 _Philip Mizzi_, Jul 25 2019 %E A309354 More terms from _Giovanni Resta_, Jul 25 2019