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A336408 a(n) = number of composites c+d such that c is a composite and d is the n-th odd composite.

%I A336408 #8 Sep 26 2020 11:45:40
%S A336408 1,4,7,8,10,13,15,17,20,22,24,24,26,31,33,35,38,40,43,44,46,47,49,52,
%T A336408 53,58,63,63,64,66,66,68,71,73,75,77,79,80,82,84,89,91,91,94,98,99,
%U A336408 102,103,105,109,110,111,114,117,120,122,123,125,128,129,131,131
%N A336408 a(n) = number of composites c+d such that c is a composite and d is the n-th odd composite.
%C A336408 The n-th odd composite is A014076(n+1); the n-th composite is A002808(n).
%e A336408 a(1) counts this sum: 6+9.
%e A336408 a(2) counts these sums: 6+15, 9+15, 10+15, 12+15.
%e A336408 a(3) counts these: 4+21, 6+21, 9+21, 12+21, 14+21, 15+21, 18+21.
%t A336408 z = 400; p = Prime[Range[z]];
%t A336408 c = Select[Range[2, z], ! PrimeQ@# &];  (* A002808 *)
%t A336408 d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
%t A336408 f[n_] := Select[c, # < d[[n]] &];
%t A336408 g[n_] := d[[n]] + Select[c, # < d[[n]] &];
%t A336408 q[n_] := Length[Intersection[p, g[n]]];
%t A336408 tq = Table[q[n], {n, 1, 120}] (* A336406 *)
%t A336408 tc = Table[Length[f[n]], {n, 1, 120}] (* A336407 *)
%t A336408 m = Min[Length[tq], Length[tc]]; Take[tc, m] - Take[tq, m] (* A336408 *)
%Y A336408 Cf. A000040, A002808, A014076, A336406, A336407.
%K A336408 nonn
%O A336408 1,2
%A A336408 _Clark Kimberling_, Jul 20 2020