A336373 Primes prime(k) such that gcd(k, prime(k)+prime(k-1)) > 1.

7, 13, 19, 23, 29, 37, 41, 43, 47, 53, 61, 71, 73, 79, 89, 101, 103, 107, 113, 131, 139, 151, 163, 167, 173, 181, 193, 197, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 433, 443

Offset: 1

Author

Clark Kimberling, Oct 05 2020

Keywords

• nonn

Comments

This sequence and A336372 partition the set of odd primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n-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 A336370; 4 and 6 are in A336371; 3 and 5 are in A336372; 7 and 13 are in this sequence.
		

Crossrefs

Cf. A000040, A336366, A336370, A336371, A336372.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* A336370 *)
v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)
Prime[u]  (* A336372 *)
Prime[v]  (* A336373 *)

Extensions

Offset corrected by Mohammed Yaseen, Jul 16 2023