A336371 Numbers k such that gcd(k, prime(k) + prime(k-1)) > 1.

4, 6, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99, 100

Offset: 1

Author

Clark Kimberling, Oct 04 2020

Keywords

• nonn

Crossrefs

Cf. A000040, A001043, A336366, A336370, A336372, 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]  (* A336372 *)
Prime[v]  (* A336373 *)

Formula

In the following table, p(k) = A000040(k) = prime(k).

k p(k) p(k)+p(k-1) gcd

2 3 5 1

3 5 8 1

4 7 12 4

5 11 18 1

6 13 24 6

2 and 3 are in A336370; 4 and 6 are in this sequence; 3 and 5 are in A336372; 7 and 13 are in A336373.

Extensions

Offset corrected by Mohammed Yaseen, Jun 02 2023