A336376 Primes p(n) such that gcd(n, prime(n)+prime(n+2)) = 1.

2, 5, 11, 17, 31, 41, 47, 59, 67, 83, 103, 109, 127, 149, 157, 167, 179, 191, 211, 227, 241, 257, 277, 283, 307, 313, 331, 347, 353, 367, 389, 401, 419, 431, 439, 449, 461, 467, 487, 499, 509, 523, 547, 563, 587, 599, 617, 631, 653, 661, 709, 727, 739, 761

Offset: 1

Author

Clark Kimberling, Oct 06 2020

Keywords

• nonn

Comments

This sequence and A336377 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, A336377.

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 *)