A355159 - OEIS

%I #19 Aug 03 2022 18:57:19

%S 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,

%T 37,38,42,47,49,51,56,57,59,61,62,63,64,65,66,67,69,71,79,81,83,87,91,

%U 92,94,97,98,99,100,101,102,103,106,108,111,112,113,114,115

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

%C 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.

%t Select[-1 + Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &]  (* A355159 *)

%t Select[-1 + Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &]  (* A355160 *)

%o (PARI) isok(k) = frac(k^(3/2)) < 1/2; \\ _Michel Marcus_, Jul 11 2022

%o (Python)

%o from math import isqrt

%o from itertools import count, islice

%o def A355159_gen(startvalue=0): # generator of terms >= startvalue

%o     return filter(lambda n:int(((r:=n**3)-(m:=isqrt(r))*(m+1))<<2<=1),count(max(startvalue,0)))

%o A355159_list = list(islice(A355159_gen(),30)) # _Chai Wah Wu_, Aug 03 2022

%Y Cf. A000093, A355160 (complement).

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 22 2022