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 A355168 #5 Jul 10 2022 16:43:54 %S A355168 1,5,8,11,27,36,52,58,64,70,76,89,96,103,110,125,140,148,156,164,181, %T A355168 198,207,216,225,234,272,322,343,364,419,430,453,476,488,500,512,524, %U A355168 536,548,573,598,702,729,756,811,868,882,911,955,970,985,1000,1015 %N A355168 Numerators of best lower approximates h/k to sqrt(k); complement of A355169. %C A355168 See A355159. %F A355168 a(n) = floor(m^(3/2)), where m = A355159(n). %e A355168 The first five best lower approximates (to sqrt(1), sqrt(3), sqrt(4), sqrt(5), sqrt(9), respectively) are 1/1, 5/3, 8/4, 11/5, 27/9; these are A355168(n)/A355159(n), for n=1..5.. %t A355168 u = Select[Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &] (* A355159 *) %t A355168 v = Select[Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &] (* A355160 *) %t A355168 Floor[u^(3/2)] (* A355168: numerators for fractions h/k <= sqrt(k) *) %t A355168 Floor[v^(3/2)] (* A355169: numerators for fractions h/k > sqrt(k) *) %Y A355168 Cf. A355159, A355160, A355169, A355115. %K A355168 nonn,easy %O A355168 1,2 %A A355168 _Clark Kimberling_, Jun 26 2022