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 A307563 #24 Jul 21 2021 00:42:47 %S A307563 1,2,4,5,9,10,12,15,17,22,25,29,32,39,44,45,60,65,67,72,75,80,82,94, %T A307563 95,99,100,109,114,117,120,124,127,137,152,155,164,169,172,177,185, %U A307563 194,199,204,205,214,215,220,229,240,242,247,254,260,262,267,269,270,289,304,312,330,334,347,355,359,369,374,379,389 %N A307563 Numbers k such that both 6k - 1 and 6k + 7 are prime. %C A307563 There are 140 such numbers between 1 and 1000. %C A307563 These numbers correspond to all the prime pairs which differ by 8 except 3 and 11. %C A307563 Numbers in this sequence are those which are not 6cd - c - d - 1, 6cd + c - d, 6cd - c + d or 6cd + c + d - 1, that is, they are not (6c - 1)d - c - 1, (6c - 1)d + c, (6c + 1)d - c or (6c + 1)d + c - 1. %H A307563 Robert Israel, <a href="/A307563/b307563.txt">Table of n, a(n) for n = 1..10000</a> %H A307563 Sally M. Moite, <a href="http://vixra.org/abs/1903.0353">“Primeless” Sieves for Primes and for Prime Pairs Which Differ by 2m</a>, vixra:1903.0353 (2019). %e A307563 a(4) = 5, so 6(5) - 1 = 29 and 6(5) + 7 = 37 are both prime. %p A307563 select(t -> isprime(6*t-1) and isprime(6*t+7), [$1..500]); # _Robert Israel_, May 27 2019 %o A307563 (PARI) isok(n) = isprime(6*n-1) && isprime(6*n+7); \\ _Michel Marcus_, Apr 16 2019 %Y A307563 The primes are A023202, A092402, A031926. %Y A307563 Similar sequences for twin primes are A002822, A067611, for "cousin" primes A056956, A186243. %Y A307563 Intersection of A024898 and A153218. %Y A307563 Cf. also A307561, A307562. %K A307563 nonn %O A307563 1,2 %A A307563 _Sally Myers Moite_, Apr 14 2019