A336370 - OEIS

%I #16 Jul 19 2023 15:16:45

%S 2,3,5,7,11,17,19,23,25,29,31,33,35,37,41,43,47,49,53,55,59,61,67,71,

%T 73,75,77,79,83,85,87,89,91,97,101,103,107,109,111,113,119,125,127,

%U 131,133,137,139,143,145,149,151,155,157,161,163,165,167,169,171

%N Numbers k such that gcd(k, prime(k) + prime(k-1)) = 1.

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

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

%e   2     3         5          1

%e   3     5         8          1

%e   4     7        12          4

%e   5    11        18          1

%e   6    13        24          6

%e 2 and 3 are in this sequence; 4 and 6 are in A336371; 3 and 5 are in A336372; 7 and 13 are in A336373.

%t p[n_] := Prime[n];

%t u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* this sequence *)

%t v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)

%t Prime[u]  (* A336372 *)

%t Prime[v]  (* A336373 *)

%Y Cf. A000040, A001043, A336366, A336371, A336372, A336373.

%K nonn

%O 1,1

%A _Clark Kimberling_, Oct 04 2020

%E Offset corrected by _Mohammed Yaseen_, Jun 02 2023