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Numbers k such that gcd(k, prime(k) + prime(k-1)) > 1.
4

%I #13 Jul 15 2023 17:49:12

%S 4,6,8,9,10,12,13,14,15,16,18,20,21,22,24,26,27,28,30,32,34,36,38,39,

%T 40,42,44,45,46,48,50,51,52,54,56,57,58,60,62,63,64,65,66,68,69,70,72,

%U 74,76,78,80,81,82,84,86,88,90,92,93,94,95,96,98,99,100

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

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

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

%F 2 3 5 1

%F 3 5 8 1

%F 4 7 12 4

%F 5 11 18 1

%F 6 13 24 6

%F 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.

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

%t u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &] (* A336370 *)

%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, A336370, A336372, A336373.

%K nonn

%O 1,1

%A _Clark Kimberling_, Oct 04 2020

%E Offset corrected by _Mohammed Yaseen_, Jun 02 2023