A355160 Numbers k such that (fractional part of k^(3/2)) > 1/2.

2, 6, 7, 8, 10, 12, 13, 19, 24, 26, 31, 33, 39, 40, 41, 43, 44, 45, 46, 48, 50, 52, 53, 54, 55, 58, 60, 68, 70, 72, 73, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 88, 89, 90, 93, 95, 96, 104, 105, 107, 109, 110, 117, 118, 120, 122, 124, 125, 132, 133, 135, 137

Offset: 1

Author

Clark Kimberling, Jun 23 2022

Keywords

• nonn
• easy

Comments

For each positive integer K there is a greatest integer h such that h/K < sqrt(K); a(n) is the n-th number h such that (h+1)/K is closer to sqrt(K) than h/K is.

Crossrefs

Cf. A000093, A355159 (complement).

Programs

Mathematica

Select[Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &]  (* A355159 *)
Select[Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &]  (* A355160 *)

PARI

isok(k) = frac(k^(3/2)) > 1/2; \\ Michel Marcus, Jul 11 2022

Python

from math import isqrt
from itertools import count, islice
def A355160_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:int(((r:=n**3)-(m:=isqrt(r))*(m+1))<<2>1),count(max(startvalue,0)))
A355160_list = list(islice(A355160_gen(),30)) # Chai Wah Wu, Aug 03 2022