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 A336368 #4 Oct 04 2020 23:34:20 %S A336368 2,11,17,23,31,41,59,67,73,83,97,109,127,157,167,179,191,211,227,233, %T A336368 241,277,283,331,353,367,389,401,431,439,461,467,499,509,523,547,563, %U A336368 587,599,607,617,631,653,661,677,691,709,727,739,751,773,797,829,859 %N A336368 Primes p(n) such that gcd(n, prime(n)+prime(n+1)) = 1. %C A336368 This sequence and A336369 partition the set of primes. %e A336368 In the following table, p(n) = A000040(n) = prime(n). %e A336368 n p(n) p(n)+p(n+1) gcd %e A336368 1 2 5 1 %e A336368 2 3 8 4 %e A336368 3 5 12 3 %e A336368 4 7 18 2 %e A336368 5 11 24 1 %e A336368 6 13 30 6 %e A336368 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 A336368 p[n_] := Prime[n]; %t A336368 u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &] (* A336366 *) %t A336368 v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &] (* A336367 *) %t A336368 Prime[u] (* A336368 *) %t A336368 Prime[v] (* A336369 *) %Y A336368 Cf. A000040, A336366, A336367, A336369. %K A336368 nonn %O A336368 1,1 %A A336368 _Clark Kimberling_, Oct 04 2020