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 A336378 #15 Jul 16 2023 17:25:50 %S A336378 2,3,7,13,17,19,23,27,29,31,37,41,43,45,47,49,53,55,59,61,63,65,67,69, %T A336378 71,73,77,79,81,83,85,89,91,93,95,97,101,103,107,109,111,113,117,119, %U A336378 121,125,127,131,133,135,137,139,141,143,145,147,149,151,157 %N A336378 Numbers k such that gcd(k, prime(k-1) + prime(k+1)) = 1. %e A336378 In the following table, p(k) = A000040(k) = prime(k). %e A336378 k p(k) p(k-1)+p(k+1) gcd %e A336378 2 3 7 1 %e A336378 3 5 10 1 %e A336378 4 7 16 4 %e A336378 5 11 20 5 %e A336378 6 13 28 2 %e A336378 2 and 3 are in this sequence; 4 and 5 are in A336379; 3 and 5 are in A336380; 7 and 11 are in A336381. %t A336378 p[n_] := Prime[n]; %t A336378 u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &] (* A336378 *) %t A336378 v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &] (* A336379 *) %t A336378 Prime[u] (* A336380 *) %t A336378 Prime[v] (* A336381 *) %Y A336378 Cf. A000040, A336366, A336379, A336380, A336381. %K A336378 nonn %O A336378 1,1 %A A336378 _Clark Kimberling_, Oct 06 2020 %E A336378 Offset corrected by _Mohammed Yaseen_, Jul 16 2023