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%I #15 Jul 16 2023 17:25:50
%S 2,3,7,13,17,19,23,27,29,31,37,41,43,45,47,49,53,55,59,61,63,65,67,69,
%T 71,73,77,79,81,83,85,89,91,93,95,97,101,103,107,109,111,113,117,119,
%U 121,125,127,131,133,135,137,139,141,143,145,147,149,151,157
%N Numbers k such that gcd(k, prime(k-1) + prime(k+1)) = 1.
%e In the following table, p(k) = A000040(k) = prime(k).
%e k p(k) p(k-1)+p(k+1) gcd
%e 2 3 7 1
%e 3 5 10 1
%e 4 7 16 4
%e 5 11 20 5
%e 6 13 28 2
%e 2 and 3 are in this sequence; 4 and 5 are in A336379; 3 and 5 are in A336380; 7 and 11 are in A336381.
%t p[n_] := Prime[n];
%t u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &] (* A336378 *)
%t v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &] (* A336379 *)
%t Prime[u] (* A336380 *)
%t Prime[v] (* A336381 *)
%Y Cf. A000040, A336366, A336379, A336380, A336381.
%K nonn
%O 1,1
%A _Clark Kimberling_, Oct 06 2020
%E Offset corrected by _Mohammed Yaseen_, Jul 16 2023
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