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 A336375 #8 Apr 21 2021 03:47:41 %S A336375 2,4,6,8,9,10,12,14,16,18,20,21,22,24,25,26,28,30,32,33,34,36,38,40, %T A336375 42,44,45,46,48,50,51,52,54,56,57,58,60,62,64,66,68,70,72,74,75,76,78, %U A336375 80,82,84,86,88,90,92,94,96,98,100,102,104,105,106,108,110 %N A336375 Numbers k such that gcd(k, prime(k) + prime(k+2)) > 1. %C A336375 This sequence and A336374 partition the positive integers. %e A336375 In the following table, p(k) = A000040(k) = prime(k). %e A336375 k p(k) p(k)+p(k+2) gcd %e A336375 1 2 7 1 %e A336375 2 3 10 2 %e A336375 3 5 16 1 %e A336375 4 7 20 4 %e A336375 5 11 28 1 %e A336375 6 13 32 2 %e A336375 1 and 3 are in A336374; 2 and 4 are in this sequence; 2 and 5 are in A336376; 3 and 7 are in A336377. %t A336375 p[n_] := Prime[n]; %t A336375 u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &] (* A336374 *) %t A336375 v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &] (* A336375 *) %t A336375 Prime[u] (* A336376 *) %t A336375 Prime[v] (* A336377 *) %Y A336375 Cf. A000040, A336366, A336374, A336376, A336377. %K A336375 nonn %O A336375 1,1 %A A336375 _Clark Kimberling_, Oct 06 2020