A379415 a(n) = n + floor(n*r/s) + floor(n*t/s), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).

2, 5, 8, 12, 14, 17, 21, 24, 26, 30, 33, 36, 39, 42, 45, 49, 51, 54, 58, 61, 63, 66, 70, 73, 75, 79, 82, 85, 89, 91, 94, 98, 101, 103, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 138, 140, 143, 147, 150, 152, 156, 159, 162, 166, 168, 171, 175, 178, 180

Offset

1,1

Comments

This sequence and A379414 and A379416 partition the positive integers; see A184812 for a proof.

Links

Table of n, a(n) for n=1..59.

Formula

a(n) = n + floor(n/r) + floor(n*r), where r = 3^(1/4).

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 *)

Crossrefs

Cf. A184812, A379415, A379416.

Cf. also A011002, A002194, A011022.

Sequence in context: A379412 A190347 A193767 * A209295 A184813 A108311

Adjacent sequences: A379412 A379413 A379414 * A379416 A379417 A379418

Keyword

nonn

Author

Clark Kimberling, Jan 18 2025

Status

approved