A336380 Primes p(k) such that gcd(k, prime(k-1)+prime(k+1)) = 1.

3, 5, 17, 41, 59, 67, 83, 103, 109, 127, 157, 179, 191, 197, 211, 227, 241, 257, 277, 283, 307, 313, 331, 347, 353, 367, 389, 401, 419, 431, 439, 461, 467, 487, 499, 509, 547, 563, 587, 599, 607, 617, 643, 653, 661, 691, 709, 739, 751, 761, 773, 797, 811

Offset: 1

Author

Clark Kimberling, Oct 25 2020

Keywords

• nonn

Examples

			In the following table, p(n) = A000040(n) = prime(n).
  n    p(n)   p(n-1)+p(n+1)   gcd
  2     3          7           1
  3     5         10           1
  4     7         16           4
  5    11         20           5
  6    13         28           2
2 and 3 are in A336378; 4 and 5 are in A336379; 3 and 5 are in this sequence; 7 and 11 are in A336381.
		

Crossrefs

Cf. A000040, A336366, A336378, A336379, A336381.

Programs

Mathematica

p[n_] := Prime[n];
u = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] == 1 &]  (* A336378 *)
v = Select[Range[2, 200], GCD[#, p[# - 1] + p[# + 1]] > 1 &]   (* A336379 *)
Prime[u]  (* this sequence *)
Prime[v]  (* A336381 *)

Extensions

Offset corrected by Mohammed Yaseen, Jul 17 2023