A355169 - OEIS

%I #4 Jul 10 2022 16:44:04

%S 2,14,18,22,31,41,46,82,117,132,172,189,243,252,262,281,291,301,311,

%T 332,353,374,385,396,407,441,464,560,585,610,623,636,649,662,675,688,

%U 715,742,769,783,797,825,839,853,896,925,940,1060,1075,1106,1137,1153

%N 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 See A355160.

%F a(n) = floor(m^(3/2)), where m = A355160(n).

%e a(1) = 2 corresponds to 2/2 < sqrt(2) < 3/2.

%e a(2) = 14 corresponds to 14/6 < sqrt(6) < 15/6.

%e a(3) = 18 corresponds to 18/7 < sqrt(7) < 19/7.

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

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

%t Floor[u^(3/2)]  (* A355168: numerators for fractions h/k <= sqrt(k) *)

%t Floor[v^(3/2)]  (* A355169: numerators for fractions h/k > sqrt(k) *)

%Y Cf. A355159, A355160, A355168, A355115.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jun 26 2022