A336379 Numbers k such that gcd(k, prime(k-1) + prime(k+1)) > 1.

4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 87, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104

Offset: 1

Author

Clark Kimberling, Oct 06 2020

Keywords

• nonn

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k-1)+p(k+1)   gcd
  2     3          7           1
  3     5         10           1
  4     7         16           4
  5    11         20           5
  6    13         28           2
2 and 3 are in A336378; 4 and 5 are in this sequence; 3 and 5 are in A336380; 7 and 11 are in A336381.
		

Crossrefs

Cf. A000040, A336366, A336378, A336380, A336381.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &]  (* A336378 *)
v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &]   (* this sequence *)
Prime[u]  (* A336380 *)
Prime[v]  (* A336381 *)

Extensions

Offset corrected by Mohammed Yaseen, Jul 16 2023