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 A355169 #4 Jul 10 2022 16:44:04 %S A355169 2,14,18,22,31,41,46,82,117,132,172,189,243,252,262,281,291,301,311, %T A355169 332,353,374,385,396,407,441,464,560,585,610,623,636,649,662,675,688, %U A355169 715,742,769,783,797,825,839,853,896,925,940,1060,1075,1106,1137,1153 %N A355169 Numbers h such that (h+1)/k is closer to sqrt(k) than h/k is, where h is the greatest integer j such that j/k < sqrt(k); complement of A355168. %C A355169 See A355160. %F A355169 a(n) = floor(m^(3/2)), where m = A355160(n). %e A355169 a(1) = 2 corresponds to 2/2 < sqrt(2) < 3/2. %e A355169 a(2) = 14 corresponds to 14/6 < sqrt(6) < 15/6. %e A355169 a(3) = 18 corresponds to 18/7 < sqrt(7) < 19/7. %t A355169 u = Select[Range[300], N[FractionalPart[#^(3/2)]] < 1/2 &] (* A355159 *) %t A355169 v = Select[Range[300], N[FractionalPart[#^(3/2)]] > 1/2 &] (* A355160 *) %t A355169 Floor[u^(3/2)] (* A355168: numerators for fractions h/k <= sqrt(k) *) %t A355169 Floor[v^(3/2)] (* A355169: numerators for fractions h/k > sqrt(k) *) %Y A355169 Cf. A355159, A355160, A355168, A355115. %K A355169 nonn,easy %O A355169 1,1 %A A355169 _Clark Kimberling_, Jun 26 2022