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 A336379 #16 Jul 17 2023 01:04:49 %S A336379 4,5,6,8,9,10,11,12,14,15,16,18,20,21,22,24,25,26,28,30,32,33,34,35, %T A336379 36,38,39,40,42,44,46,48,50,51,52,54,56,57,58,60,62,64,66,68,70,72,74, %U A336379 75,76,78,80,82,84,86,87,88,90,92,94,96,98,99,100,102,104 %N A336379 Numbers k such that gcd(k, prime(k-1) + prime(k+1)) > 1. %e A336379 In the following table, p(k) = A000040(k) = prime(k). %e A336379 k p(k) p(k-1)+p(k+1) gcd %e A336379 2 3 7 1 %e A336379 3 5 10 1 %e A336379 4 7 16 4 %e A336379 5 11 20 5 %e A336379 6 13 28 2 %e A336379 2 and 3 are in A336378; 4 and 5 are in this sequence; 3 and 5 are in A336380; 7 and 11 are in A336381. %t A336379 p[n_] := Prime[n]; %t A336379 u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &] (* A336378 *) %t A336379 v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &] (* this sequence *) %t A336379 Prime[u] (* A336380 *) %t A336379 Prime[v] (* A336381 *) %Y A336379 Cf. A000040, A336366, A336378, A336380, A336381. %K A336379 nonn %O A336379 1,1 %A A336379 _Clark Kimberling_, Oct 06 2020 %E A336379 Offset corrected by _Mohammed Yaseen_, Jul 16 2023