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

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

1,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.

Maple

Comps:= remove(isprime, [$4..10^5]):
OComps:= select(type, Comps, odd):
f:= proc(n) local d, m;
   d:= OComps[n];
   m:= ListTools:-BinarySearch(Comps, d);
   nops(remove(c -> isprime(c+d), Comps[1..m-1]))
end proc:
map(f, [$1..100]); # Robert Israel, Jun 07 2026

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 *)

Crossrefs

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

Sequence in context: A175553 A284684 A175008 * A286401 A084791 A310933

Adjacent sequences: A336405 A336406 A336407 * A336409 A336410 A336411

Keyword

nonn

Author

Clark Kimberling, Jul 20 2020

Extensions

Definition corrected by Robert Israel, Jun 07 2026

Status

approved