A379412 a(n) = n + floor(n*r/s) + floor(n*t/s), where r = e^(1/4); s = e^(1/2); t = e^(3/4).

2, 5, 8, 12, 14, 17, 20, 24, 27, 29, 33, 36, 39, 41, 45, 48, 51, 55, 57, 60, 63, 67, 69, 72, 76, 79, 82, 84, 88, 91, 94, 97, 100, 103, 106, 110, 112, 115, 119, 122, 124, 127, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 162, 165, 167, 170, 174, 177, 179

Offset: 1

Author

Clark Kimberling, Jan 15 2025

Keywords

• nonn

Comments

This sequence and A379411 and A379413 partition the positive integers.

Crossrefs

Cf. A001113, A378142, A379411, A379413.

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), where r = e^(1/4).