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