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