A379416 a(n) = n + [n*r/t] + [n*s/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.

1, 4, 6, 9, 10, 13, 16, 18, 20, 22, 25, 27, 29, 32, 34, 37, 38, 41, 43, 46, 48, 50, 53, 55, 57, 60, 62, 65, 67, 69, 71, 74, 77, 78, 81, 83, 86, 87, 90, 93, 95, 97, 99, 102, 104, 106, 109, 111, 114, 115, 118, 121, 123, 126, 127, 130, 132, 135, 137, 139, 142

Offset: 1

Author

Clark Kimberling, Jan 20 2025

Keywords

• nonn

Comments

This sequence and A379414 and A379415 partition the positive integers; see A184812 for a proof.

Crossrefs

Cf. A184812, A379414, A379415.

Programs

Mathematica

r = 3^(1/4); s = 3^(1/2); t = 3^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379414 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379415 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379416 *)

Formula

a(n) = n + [n*r/t] + [n*s/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.

a(n) = n + [n/r] + [n/r^2], where r = 3^(1/4) and [ ] = floor.