A379409 a(n) = n + floor(n*r/s) + floor(n*t/s), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).

2, 5, 8, 11, 14, 17, 20, 24, 26, 29, 32, 35, 38, 41, 44, 48, 51, 53, 56, 59, 62, 65, 68, 72, 75, 78, 80, 83, 86, 89, 92, 96, 99, 102, 105, 107, 110, 113, 116, 120, 123, 126, 129, 132, 134, 137, 141, 144, 147, 150, 153, 156, 158, 161, 165, 168, 171, 174, 177

Offset

1,1

Comments

This sequence and A379408 and A379410 partition the positive integers.

Links

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

Formula

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

Mathematica

u = (1 + 5^(1/2))/2;
r = u^(1/4); s = u^(1/2); t = u^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379408 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379409 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379410 *)

Crossrefs

Cf. A001622, A379408, A379410.

Sequence in context: A379418 A190361 A184905 * A279773 A184910 A190006

Adjacent sequences: A379406 A379407 A379408 * A379410 A379411 A379412

Keyword

nonn

Author

Clark Kimberling, Jan 15 2025

Status

approved