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 A336373 #10 Jul 16 2023 10:36:33 %S A336373 7,13,19,23,29,37,41,43,47,53,61,71,73,79,89,101,103,107,113,131,139, %T A336373 151,163,167,173,181,193,197,199,223,229,233,239,251,263,269,271,281, %U A336373 293,307,311,313,317,337,347,349,359,373,383,397,409,419,421,433,443 %N A336373 Primes prime(k) such that gcd(k, prime(k)+prime(k-1)) > 1. %C A336373 This sequence and A336372 partition the set of odd primes. %e A336373 In the following table, p(n) = A000040(n) = prime(n). %e A336373 n p(n) p(n)+p(n-1) gcd %e A336373 2 3 5 1 %e A336373 3 5 8 1 %e A336373 4 7 12 4 %e A336373 5 11 18 1 %e A336373 6 13 24 6 %e A336373 2 and 3 are in A336370; 4 and 6 are in A336371; 3 and 5 are in A336372; 7 and 13 are in this sequence. %t A336373 p[n_] := Prime[n]; %t A336373 u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &] (* A336370 *) %t A336373 v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &] (* A336371 *) %t A336373 Prime[u] (* A336372 *) %t A336373 Prime[v] (* A336373 *) %Y A336373 Cf. A000040, A336366, A336370, A336371, A336372. %K A336373 nonn %O A336373 1,1 %A A336373 _Clark Kimberling_, Oct 05 2020 %E A336373 Offset corrected by _Mohammed Yaseen_, Jul 16 2023