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

1, 4, 7, 8, 10, 13, 15, 17, 20, 22, 24, 24, 26, 31, 33, 35, 38, 40, 43, 44, 46, 47, 49, 52, 53, 58, 63, 63, 64, 66, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 89, 91, 91, 94, 98, 99, 102, 103, 105, 109, 110, 111, 114, 117, 120, 122, 123, 125, 128, 129, 131, 131

Offset: 1

Author

Clark Kimberling, Jul 20 2020

Keywords

• nonn

Comments

The n-th odd composite is A014076(n+1); the n-th composite is A002808(n).

Examples

			a(1) counts this sum: 6+9.
a(2) counts these sums: 6+15, 9+15, 10+15, 12+15.
a(3) counts these: 4+21, 6+21, 9+21, 12+21, 14+21, 15+21, 18+21.
		

Crossrefs

Cf. A000040, A002808, A014076, A336406, A336407.

Programs

Mathematica

z = 400; p = Prime[Range[z]];
c = Select[Range[2, z], ! PrimeQ@# &];  (* A002808 *)
d = Select[Range[2, z], ! PrimeQ@# && OddQ@# &];  (* A014076 *)
f[n_] := Select[c, # < d[[n]] &];
g[n_] := d[[n]] + Select[c, # < d[[n]] &];
q[n_] := Length[Intersection[p, g[n]]];
tq = Table[q[n], {n, 1, 120}] (* A336406 *)
tc = Table[Length[f[n]], {n, 1, 120}] (* A336407 *)
m = Min[Length[tq], Length[tc]]; Take[tc, m] - Take[tq, m] (* A336408 *)