A336372 Primes prime(k) such that gcd(k, prime(k) + prime(k-1)) = 1.

3, 5, 11, 17, 31, 59, 67, 83, 97, 109, 127, 137, 149, 157, 179, 191, 211, 227, 241, 257, 277, 283, 331, 353, 367, 379, 389, 401, 431, 439, 449, 461, 467, 509, 547, 563, 587, 599, 607, 617, 653, 691, 709, 739, 751, 773, 797, 823, 829, 859, 877, 907, 919, 947

Offset: 1

Author

Clark Kimberling, Oct 05 2020

Keywords

• nonn

Comments

This sequence and A336373 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
		

Crossrefs

Cf. A000040, A001043, A336366, A336370, A336371, A336373.

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]  (* this sequence *)
Prime[v]  (* A336373 *)

Extensions

Offset corrected by Mohammed Yaseen, Jun 02 2023