A379422 a(n) = n + floor(n*r/t) + floor(n*s/t), where r = 5^(1/4), s = 5^(1/2), t = 5^(3/4).

1, 3, 6, 7, 10, 12, 14, 16, 19, 20, 22, 25, 26, 29, 31, 33, 35, 38, 39, 41, 44, 45, 48, 50, 52, 54, 57, 58, 60, 63, 64, 67, 69, 71, 73, 76, 77, 79, 82, 83, 86, 88, 90, 92, 95, 96, 99, 101, 102, 105, 107, 109, 111, 114, 115, 118, 120, 121, 124, 126, 128, 130

Offset

1,2

Comments

This sequence and A379420 and A379421 partition the positive integers; see A184812 for a proof.

Links

Table of n, a(n) for n=1..62.

Formula

a(n) = n + floor(n/r) + floor(n/r^2), where r = 5^(1/4).

Mathematica

r = 5^(1/4); s = 5^(1/2); t = 5^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379420 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379421 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379422 *)

Crossrefs

Cf. A184812, A379420, A379421.

Sequence in context: A084463 A096604 A184873 * A184903 A330180 A330184

Adjacent sequences: A379419 A379420 A379421 * A379423 A379424 A379425

Keyword

nonn

Author

Clark Kimberling, Jan 21 2025

Status

approved