A379413 a(n) = n + floor(n*r/t) + floor(n*s/t), where r = e^(1/4), s = e^(1/2), t = e^(3/4).

1, 4, 6, 9, 11, 13, 16, 18, 21, 23, 25, 28, 30, 32, 35, 37, 40, 42, 44, 47, 49, 52, 53, 56, 59, 61, 64, 65, 68, 71, 73, 75, 78, 80, 83, 85, 87, 90, 92, 95, 96, 99, 102, 104, 107, 108, 111, 114, 116, 118, 120, 123, 126, 128, 130, 132, 135, 138, 139, 142, 144

Offset: 1

Author

Clark Kimberling, Jan 18 2025

Keywords

• nonn

Comments

This sequence and A379411 and A379412 partition the positive integers; see A378142 for a proof.

Crossrefs

Cf. A378142, A379411, A379412.

Cf. A092042, A019774, A331501.

Programs

Mathematica

r = E^(1/4); s = E^(1/2); t = E^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379411 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379412 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379413 *)

Formula

a(n) = n + floor(n/r) + floor(n*r^2), where r = e^(1/4).