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 A336377 #4 Oct 18 2020 22:36:33 %S A336377 3,7,13,19,23,29,37,43,53,61,71,73,79,89,97,101,107,113,131,137,139, %T A336377 151,163,173,181,193,197,199,223,229,233,239,251,263,269,271,281,293, %U A336377 311,317,337,349,359,373,379,383,397,409,421,433,443,457,463,479,491 %N A336377 Primes p(n) such that gcd(n, prime(n)+prime(n+2)) > 1. %C A336377 This sequence and A336376 partition the set of primes. %e A336377 In the following table, p(n) = A000040(n) = prime(n). %e A336377 n p(n) p(n)+p(n+2) gcd %e A336377 1 2 7 1 %e A336377 2 3 10 2 %e A336377 3 5 16 1 %e A336377 4 7 20 4 %e A336377 5 11 28 1 %e A336377 6 13 32 2 %e A336377 1 and 3 are in A336374; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377. %t A336377 p[n_] := Prime[n]; %t A336377 u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &] (* A336374 *) %t A336377 v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &] (* A336375 *) %t A336377 Prime[u] (* A336376 *) %t A336377 Prime[v] (* A336377 *) %Y A336377 Cf. A000040, A336366, A336374, A336375, A336376. %K A336377 nonn %O A336377 1,1 %A A336377 _Clark Kimberling_, Oct 06 2020