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

1,1

Comments

See A355160.

Links

Table of n, a(n) for n=1..52.

Formula

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

Example

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.

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, A355168, A355115.

Sequence in context: A278975 A096508 A374584 * A108029 A212048 A322955

Adjacent sequences: A355166 A355167 A355168 * A355170 A355171 A355172

Keyword

nonn,easy

Author

Clark Kimberling, Jun 26 2022

Status

approved