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 A336369 #4 Oct 04 2020 23:34:32 %S A336369 3,5,7,13,19,29,37,43,47,53,61,71,79,89,101,103,107,113,131,137,139, %T A336369 149,151,163,173,181,193,197,199,223,229,239,251,257,263,269,271,281, %U A336369 293,307,311,313,317,337,347,349,359,373,379,383,397,409,419,421,433 %N A336369 Primes p(n) such that gcd(n, prime(n)+prime(n+1)) > 1. %C A336369 This sequence and A336368 partition the set of primes. %e A336369 In the following table, p(n) = A000040(n) = prime(n). %e A336369 n p(n) p(n)+p(n+1) gcd %e A336369 1 2 5 1 %e A336369 2 3 8 4 %e A336369 3 5 12 3 %e A336369 4 7 18 2 %e A336369 5 11 24 1 %e A336369 6 13 30 6 %e A336369 1 and 5 are in A336366; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369. %t A336369 p[n_] := Prime[n]; %t A336369 u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &] (* A336366 *) %t A336369 v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &] (* A336367 *) %t A336369 Prime[u] (* A336368 *) %t A336369 Prime[v] (* A336369 *) %Y A336369 Cf. A000040, A336366, A336367, A336368. %K A336369 nonn %O A336369 1,1 %A A336369 _Clark Kimberling_, Oct 04 2020