A379418 a(n) = n + [n*r/s] + [n*t/s], where r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4) and [ ] = floor.

2, 5, 8, 11, 14, 17, 20, 23, 26, 30, 32, 35, 38, 41, 44, 47, 50, 53, 57, 60, 62, 65, 68, 71, 74, 77, 80, 83, 87, 90, 93, 95, 98, 101, 104, 107, 110, 114, 117, 120, 123, 125, 128, 131, 134, 137, 141, 144, 147, 150, 153, 155, 158, 161, 164, 167, 171, 174, 177

Offset

1,1

Comments

This sequence and A379417 and A379419 partition the positive integers; see A184812 for a proof.

Links

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

Formula

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

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

Mathematica

r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379417 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379418 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379419 *)

Crossrefs

Cf. A184812, A379417, A379419.

Sequence in context: A190082 A165334 A189512 * A190361 A184905 A379409

Adjacent sequences: A379415 A379416 A379417 * A379419 A379420 A379421

Keyword

nonn

Author

Clark Kimberling, Jan 20 2025

Status

approved