A355159 Numbers k such that (fractional part of k^(3/2)) < 1/2.

0, 1, 3, 4, 5, 9, 11, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 27, 28, 29, 30, 32, 34, 35, 36, 37, 38, 42, 47, 49, 51, 56, 57, 59, 61, 62, 63, 64, 65, 66, 67, 69, 71, 79, 81, 83, 87, 91, 92, 94, 97, 98, 99, 100, 101, 102, 103, 106, 108, 111, 112, 113, 114, 115

Offset: 0

Author

Clark Kimberling, Jun 22 2022

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A000093, A355160 (complement).

Programs

Mathematica

Select[-1 + Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &]  (* A355159 *)
Select[-1 + 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 A355159_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)))
A355159_list = list(islice(A355159_gen(),30)) # Chai Wah Wu, Aug 03 2022