A336370 Numbers k such that gcd(k, prime(k) + prime(k-1)) = 1.

2, 3, 5, 7, 11, 17, 19, 23, 25, 29, 31, 33, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 67, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 97, 101, 103, 107, 109, 111, 113, 119, 125, 127, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 161, 163, 165, 167, 169, 171

Offset: 1

Author

Clark Kimberling, Oct 04 2020

Keywords

• nonn

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k)+p(k-1)   gcd
  2     3         5          1
  3     5         8          1
  4     7        12          4
  5    11        18          1
  6    13        24          6
2 and 3 are in this sequence; 4 and 6 are in A336371; 3 and 5 are in A336372; 7 and 13 are in A336373.
		

Crossrefs

Cf. A000040, A001043, A336366, A336371, A336372, A336373.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* this sequence *)
v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)
Prime[u]  (* A336372 *)
Prime[v]  (* A336373 *)

Extensions

Offset corrected by Mohammed Yaseen, Jun 02 2023