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A336406 a(n) = number of primes c + d, where c < d = odd composite(n), and c is composite.

%I A336406 #5 Sep 04 2020 15:43:40
%S A336406 2,3,4,6,6,7,7,8,9,10,10,13,13,12,12,13,14,14,14,16,16,18,18,17,19,18,
%T A336406 17,20,21,21,23,23,22,23,24,24,26,27,27,27,26,26,29,28,27,29,28,30,30,
%U A336406 30,31,32,31,32,33,33,34,34,33,35,35,37,37,37,38,38,40
%N A336406 a(n) = number of primes c + d, where c < d  = odd composite(n), and c is composite.
%e A336406 The 5th odd composite is 27, so that a(5) counts these 6 primes:
%e A336406 4 + 27, 10 + 27, 14 + 27, 16 + 27, 20 + 27, 26 + 27.
%t A336406 z = 400; p = Prime[Range[z]];
%t A336406 c = Select[Range[2, z], ! PrimeQ@# &];  (* A002808 *)
%t A336406 d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
%t A336406 f[n_] := Select[c, # < d[[n]] &];
%t A336406 g[n_] := d[[n]] + Select[c, # < d[[n]] &];
%t A336406 q[n_] := Length[Intersection[p, g[n]]];
%t A336406 tq = Table[q[n], {n, 1, 120}] (* A336406 *)
%t A336406 tc = Table[Length[f[n]], {n, 1, 120}] (* A336407 *)
%t A336406 m = Min[Length[tq], Length[tc]]; Take[tc, m] - Take[tq, m] (* A336408 *)
%Y A336406 Cf. A000040, A002808, A014076, A336407, A336408.
%K A336406 nonn
%O A336406 1,1
%A A336406 _Clark Kimberling_, Jul 20 2020