This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355159 #19 Aug 03 2022 18:57:19 %S A355159 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 A355159 37,38,42,47,49,51,56,57,59,61,62,63,64,65,66,67,69,71,79,81,83,87,91, %U A355159 92,94,97,98,99,100,101,102,103,106,108,111,112,113,114,115 %N A355159 Numbers k such that (fractional part of k^(3/2)) < 1/2. %C A355159 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 A355159 Select[-1 + Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &] (* A355159 *) %t A355159 Select[-1 + Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &] (* A355160 *) %o A355159 (PARI) isok(k) = frac(k^(3/2)) < 1/2; \\ _Michel Marcus_, Jul 11 2022 %o A355159 (Python) %o A355159 from math import isqrt %o A355159 from itertools import count, islice %o A355159 def A355159_gen(startvalue=0): # generator of terms >= startvalue %o A355159 return filter(lambda n:int(((r:=n**3)-(m:=isqrt(r))*(m+1))<<2<=1),count(max(startvalue,0))) %o A355159 A355159_list = list(islice(A355159_gen(),30)) # _Chai Wah Wu_, Aug 03 2022 %Y A355159 Cf. A000093, A355160 (complement). %K A355159 nonn,easy %O A355159 0,3 %A A355159 _Clark Kimberling_, Jun 22 2022