A336368 Primes p(n) such that gcd(n, prime(n)+prime(n+1)) = 1.

2, 11, 17, 23, 31, 41, 59, 67, 73, 83, 97, 109, 127, 157, 167, 179, 191, 211, 227, 233, 241, 277, 283, 331, 353, 367, 389, 401, 431, 439, 461, 467, 499, 509, 523, 547, 563, 587, 599, 607, 617, 631, 653, 661, 677, 691, 709, 727, 739, 751, 773, 797, 829, 859

Offset: 1

Author

Clark Kimberling, Oct 04 2020

Keywords

• nonn

Comments

This sequence and A336369 partition the set of primes.

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n)+p(n+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
1 and 5 are in A336366; 2 and 3 are in A336367; 2 and 11 are in A336368; 3 and 5 are in A336369.
		

Crossrefs

Cf. A000040, A336366, A336367, 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 *)