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 A336380 #11 Jul 17 2023 01:16:10 %S A336380 3,5,17,41,59,67,83,103,109,127,157,179,191,197,211,227,241,257,277, %T A336380 283,307,313,331,347,353,367,389,401,419,431,439,461,467,487,499,509, %U A336380 547,563,587,599,607,617,643,653,661,691,709,739,751,761,773,797,811 %N A336380 Primes p(k) such that gcd(k, prime(k-1)+prime(k+1)) = 1. %e A336380 In the following table, p(n) = A000040(n) = prime(n). %e A336380 n p(n) p(n-1)+p(n+1) gcd %e A336380 2 3 7 1 %e A336380 3 5 10 1 %e A336380 4 7 16 4 %e A336380 5 11 20 5 %e A336380 6 13 28 2 %e A336380 2 and 3 are in A336378; 4 and 5 are in A336379; 3 and 5 are in this sequence; 7 and 11 are in A336381. %t A336380 p[n_] := Prime[n]; %t A336380 u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &] (* A336378 *) %t A336380 v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &] (* A336379 *) %t A336380 Prime[u] (* this sequence *) %t A336380 Prime[v] (* A336381 *) %Y A336380 Cf. A000040, A336366, A336378, A336379, A336381. %K A336380 nonn %O A336380 1,1 %A A336380 _Clark Kimberling_, Oct 25 2020 %E A336380 Offset corrected by _Mohammed Yaseen_, Jul 17 2023