A336377 - OEIS

%I #4 Oct 18 2020 22:36:33

%S 3,7,13,19,23,29,37,43,53,61,71,73,79,89,97,101,107,113,131,137,139,

%T 151,163,173,181,193,197,199,223,229,233,239,251,263,269,271,281,293,

%U 311,317,337,349,359,373,379,383,397,409,421,433,443,457,463,479,491

%N Primes p(n) such that gcd(n, prime(n)+prime(n+2)) > 1.

%C This sequence and A336376 partition the set of primes.

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

%e   n    p(n)   p(n)+p(n+2)   gcd

%e   1     2         7          1

%e   2     3        10          2

%e   3     5        16          1

%e   4     7        20          4

%e   5    11        28          1

%e   6    13        32          2

%e 1 and 3 are in A336374; 2 and 4 are in A336375; 2 and 5 are in A336376; 3 and 7 are in A336377.

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

%t u = Select[Range[200], GCD[#, p[#] + p[# + 2]] == 1 &]  (* A336374 *)

%t v = Select[Range[200], GCD[#, p[#] + p[# + 2]] > 1 &]   (* A336375 *)

%t Prime[u]  (* A336376 *)

%t Prime[v]  (* A336377 *)

%Y Cf. A000040, A336366, A336374, A336375, A336376.

%K nonn

%O 1,1

%A _Clark Kimberling_, Oct 06 2020