A336366 Numbers k such that gcd(k, prime(k) + prime(k+1)) = 1.

1, 5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 37, 39, 41, 43, 47, 49, 51, 53, 59, 61, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 133, 137, 139, 145, 149, 151, 155, 157, 161, 163

Offset: 1

Author

Clark Kimberling, Jul 19 2020

Keywords

• nonn

Comments

This sequence and A336367 partition the positive integers.

Examples

			In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k)+p(k+1)   gcd
  1     2          5         1
  2     3          8         4
  3     5         12         3
  4     7         18         2
  5    11         24         1
  6    13         30         6
Thus 1 and 5 are in this sequence; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369.
		

Crossrefs

Cf. A000040, A336367, A336368, A336369.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 1]] == 1 &] (* A336366 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 1]] > 1 &]   (* A336367 *)
Prime[u] (* A336368 *)
Prime[v] (* A336369 *)

PARI

isok(m) = gcd(m, prime(m)+prime(m+1)) == 1; \\ Michel Marcus, Jul 20 2020