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

Author

Clark Kimberling, Jun 26 2022

Keywords

• nonn
• easy

Comments

See A355159.

Examples

			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..
		

Crossrefs

Cf. A355159, A355160, A355169, A355115.

Programs

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) *)

Formula

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