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A336372 Primes prime(k) such that gcd(k, prime(k) + prime(k-1)) = 1.

%I A336372 #16 Jul 19 2023 15:17:56
%S A336372 3,5,11,17,31,59,67,83,97,109,127,137,149,157,179,191,211,227,241,257,
%T A336372 277,283,331,353,367,379,389,401,431,439,449,461,467,509,547,563,587,
%U A336372 599,607,617,653,691,709,739,751,773,797,823,829,859,877,907,919,947
%N A336372 Primes prime(k) such that gcd(k, prime(k) + prime(k-1)) = 1.
%C A336372 This sequence and A336373 partition the set of odd primes.
%e A336372 In the following table, p(n) = A000040(n) = prime(n).
%e A336372   n    p(n)   p(n)+p(n-1)   gcd
%e A336372   2     3         5          1
%e A336372   3     5         8          1
%e A336372   4     7        12          4
%e A336372   5    11        18          1
%e A336372   6    13        24          6
%t A336372 p[n_] := Prime[n];
%t A336372 u = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] == 1 &]  (* A336370 *)
%t A336372 v = Select[Range[2, 200], GCD[#, p[#] + p[# - 1]] > 1 &]   (* A336371 *)
%t A336372 Prime[u]  (* this sequence *)
%t A336372 Prime[v]  (* A336373 *)
%Y A336372 Cf. A000040, A001043, A336366, A336370, A336371, A336373.
%K A336372 nonn
%O A336372 1,1
%A A336372 _Clark Kimberling_, Oct 05 2020
%E A336372 Offset corrected by _Mohammed Yaseen_, Jun 02 2023