A355168 -id:A355168 - cp's OEIS frontend

A355169 Numbers h such that (h+1)/k is closer to sqrt(k) than h/k is, where h is the greatest integer j such that j/k < sqrt(k); complement of A355168.

2, 14, 18, 22, 31, 41, 46, 82, 117, 132, 172, 189, 243, 252, 262, 281, 291, 301, 311, 332, 353, 374, 385, 396, 407, 441, 464, 560, 585, 610, 623, 636, 649, 662, 675, 688, 715, 742, 769, 783, 797, 825, 839, 853, 896, 925, 940, 1060, 1075, 1106, 1137, 1153

Offset: 1

Graph
List
Refs
Listen
History
Text
Internal format

Clark Kimberling, Jun 26 2022

nonn
easy

See A355160.

			a(1) = 2 corresponds to 2/2 < sqrt(2) < 3/2.
a(2) = 14 corresponds to 14/6 < sqrt(6) < 15/6.
a(3) = 18 corresponds to 18/7 < sqrt(7) < 19/7.

Cf. A355159, A355160, A355168, A355115.

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) *)

a(n) = floor(m^(3/2)), where m = A355160(n).

cp's OEIS Frontend

A355169 Numbers h such that (h+1)/k is closer to sqrt(k) than h/k is, where h is the greatest integer j such that j/k < sqrt(k); complement of A355168.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula