A336375 Numbers k such that gcd(k, prime(k) + prime(k+2)) > 1.

2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110

Offset

1,1

Comments

This sequence and A336374 partition the positive integers.

Links

Table of n, a(n) for n=1..64.

Example

In the following table, p(k) = A000040(k) = prime(k).
  k    p(k)   p(k)+p(k+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 this sequence; 2 and 5 are in A336376; 3 and 7 are in A336377.

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 *)

Crossrefs

Cf. A000040, A336366, A336374, A336376, A336377.

Sequence in context: A282760 A355529 A355670 * A353683 A296214 A325572

Adjacent sequences: A336372 A336373 A336374 * A336376 A336377 A336378

Keyword

nonn

Author

Clark Kimberling, Oct 06 2020

Status

approved