A379410 a(n) = n + floor(n*r/t) + floor(n*s/t), where r = u^(1/4), s = u^(1/2), t = u^(3/4), u = golden ratio (A001622).

1, 4, 7, 10, 12, 15, 18, 21, 23, 25, 28, 31, 34, 37, 39, 42, 45, 47, 49, 52, 55, 58, 61, 63, 66, 69, 71, 74, 76, 79, 82, 85, 87, 90, 93, 95, 98, 100, 103, 106, 109, 112, 114, 117, 119, 122, 124, 127, 130, 133, 136, 138, 140, 143, 146, 149, 151, 154, 157, 160, 162, 164, 167, 170

Offset

1,2

Comments

This sequence, A379408, and A379409 partition the positive integers.

Links

Table of n, a(n) for n=1..64.

Formula

a(n) = n + floor(n/r^2) + 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, A184908, A379408, A379409.

Sequence in context: A190008 A184911 A103762 * A186226 A080734 A310676

Adjacent sequences: A379407 A379408 A379409 * A379411 A379412 A379413

Keyword

nonn

Author

Clark Kimberling, Jan 21 2025

Extensions

Values corrected by R. J. Mathar, Jan 28 2025

Status

approved