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A336367 Numbers k such that gcd(k, prime(k) + prime(k+1)) > 1.

%I A336367 #8 Apr 21 2021 03:49:43
%S A336367 2,3,4,6,8,10,12,14,15,16,18,20,22,24,26,27,28,30,32,33,34,35,36,38,
%T A336367 40,42,44,45,46,48,50,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,
%U A336367 74,75,76,78,80,81,82,84,86,87,88,90,92,93,94,96,98,100
%N A336367 Numbers k such that gcd(k, prime(k) + prime(k+1)) > 1.
%C A336367 Complement of A336366.
%e A336367 In the following table, p(k) = A000040(k) = prime(k).
%e A336367   k    p(k)   p(k)+p(k+1)   gcd
%e A336367   1     2         5          1
%e A336367   2     3         8          4
%e A336367   3     5        12          3
%e A336367   4     7        18          2
%e A336367   5    11        24          1
%e A336367   6    13        30          6
%e A336367 1 and 5 are in A336366; 2 and 3 are in this sequence; 2 and 11 are in A336368; 3 and 5 are in A336369.
%t A336367 p[n_] := Prime[n];
%t A336367 u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &]  (* A336366 *)
%t A336367 v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &]   (* A336367 *)
%t A336367 Prime[u] (* A336368 *)
%t A336367 Prime[v] (* A336369 *)
%Y A336367 Cf. A000040, A336366, A336368, A336369.
%K A336367 nonn
%O A336367 1,1
%A A336367 _Clark Kimberling_, Oct 04 2020