A336377 Primes p(n) such that gcd(n, prime(n)+prime(n+2)) > 1.

3, 7, 13, 19, 23, 29, 37, 43, 53, 61, 71, 73, 79, 89, 97, 101, 107, 113, 131, 137, 139, 151, 163, 173, 181, 193, 197, 199, 223, 229, 233, 239, 251, 263, 269, 271, 281, 293, 311, 317, 337, 349, 359, 373, 379, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491

Offset: 1

Author

Clark Kimberling, Oct 06 2020

Keywords

• nonn

Comments

This sequence and A336376 partition the set of primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n+2)   gcd
  1     2         7          1
  2     3        10          2
  3     5        16          1
  4     7        20          4
  5    11        28          1
  6    13        32          2
1 and 3 are in A336374; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377.
		

Crossrefs

Cf. A000040, A336366, A336374, A336375, A336376.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &]  (* A336374 *)
v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &]   (* A336375 *)
Prime[u]  (* A336376 *)
Prime[v]  (* A336377 *)