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%I #29 Jan 22 2020 06:26:14
%S 1,2,3,4,7,8,9,14,17,18,22,28,29,32,38,39,42,43,44,52,58,59,64,74,77,
%T 84,93,94,98,99,107,108,109,113,137,143,147,157,158,162,163,169,182,
%U 183,184,197,198,203,204,213,214,217,227,228,238,239,247,248,249,259,267,268,269,312,317,318,329,333,344
%N Numbers k such that both 6*k - 1 and 6*k + 5 are prime.
%C There are 146 terms below 10^3, 831 terms below 10^4, 5345 terms below 10^5, 37788 terms below 10^6 and 280140 terms below 10^7.
%C Prime pairs differing by 6 are called "sexy" primes. Other prime pairs with difference 6 are of the form 6n + 1 and 6n + 7.
%C Numbers in this sequence are those which are not 6cd + c - d - 1, 6cd + c - d, 6cd - c + d - 1 or 6cd - c + d, that is, they are not (6c - 1)d + c - 1, (6c - 1)d + c, (6c + 1)d - c - 1 or (6c + 1)d - c.
%H Amiram Eldar, <a href="/A307561/b307561.txt">Table of n, a(n) for n = 1..10000</a>
%H 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 a(2) = 2, so 6(2) - 1 = 11 and 6(2) + 5 = 17 are both prime.
%t Select[Range[500], PrimeQ[6# - 1] && PrimeQ[6# + 5] &] (* _Alonso del Arte_, Apr 14 2019 *)
%o (PARI) is(k) = isprime(6*k-1) && isprime(6*k+5); \\ _Jinyuan Wang_, Apr 20 2019
%Y Primes differing from each other by 6 are A023201, A046117.
%Y Similar sequences for twin primes are A002822, A067611, for "cousin" primes A056956, A186243.
%Y Intersection of A024898 and A059325.
%Y Cf. also A307562, A307563.
%K nonn
%O 1,2
%A _Sally Myers Moite_, Apr 14 2019
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