A355168 Numerators of best lower approximates h/k to sqrt(k); complement of A355169.

1, 5, 8, 11, 27, 36, 52, 58, 64, 70, 76, 89, 96, 103, 110, 125, 140, 148, 156, 164, 181, 198, 207, 216, 225, 234, 272, 322, 343, 364, 419, 430, 453, 476, 488, 500, 512, 524, 536, 548, 573, 598, 702, 729, 756, 811, 868, 882, 911, 955, 970, 985, 1000, 1015

Offset

1,2

Comments

See A355159.

Links

Table of n, a(n) for n=1..54.

Formula

a(n) = floor(m^(3/2)), where m = A355159(n).

Example

The first five best lower approximates (to sqrt(1), sqrt(3), sqrt(4), sqrt(5), sqrt(9), respectively) are 1/1, 5/3, 8/4, 11/5, 27/9; these are A355168(n)/A355159(n), for n=1..5..

Mathematica

u = Select[Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &]  (* A355159 *)
v = Select[Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &]  (* A355160 *)
Floor[u^(3/2)]  (* A355168: numerators for fractions h/k <= sqrt(k) *)
Floor[v^(3/2)]  (* A355169: numerators for fractions h/k > sqrt(k) *)

Crossrefs

Cf. A355159, A355160, A355169, A355115.

Sequence in context: A162612 A314400 A314401 * A237434 A133522 A133269

Adjacent sequences: A355165 A355166 A355167 * A355169 A355170 A355171

Keyword

nonn,easy

Author

Clark Kimberling, Jun 26 2022

Status

approved