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A024832 Least m such that if r and s in {Pi/2 - atn(h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.

%I A024832 #14 Feb 26 2024 14:11:06
%S A024832 2,3,7,10,17,21,31,43,50,65,82,91,111,133,157,170,197,226,257,273,307,
%T A024832 343,381,421,442,485,530,577,626,651,703,757,813,871,931,962,1025,
%U A024832 1090,1157,1226,1297,1333,1407,1483,1561,1641,1723,1807,1850,1937,2026,2117,2210,2305
%N A024832 Least m such that if r and s in {Pi/2 - atn(h): h = 1,2,...,n} satisfy r < s, then r < k/m < s for some integer k.
%C A024832 For a guide to related sequences, see A001000. - _Clark Kimberling_, Aug 07 2012
%H A024832 Clark Kimberling, <a href="/A024832/b024832.txt">Table of n, a(n) for n = 2..200</a>
%t A024832 leastSeparator[seq_] := Module[{n = 1},
%t A024832 Table[While[Or @@ (Ceiling[n #1[[1]]] <
%t A024832 2 + Floor[n #1[[2]]] &) /@ (Sort[#1, Greater] &) /@
%t A024832 Partition[Take[seq, k], 2, 1], n++]; n, {k, 2, Length[seq]}]];
%t A024832 t = Flatten[Table[Pi/2 - ArcTan[h], {h, 1, 60}]]; leastSeparator[t]
%t A024832 (* _Peter J. C. Moses_, Aug 01 2012 *)
%Y A024832 Cf. A001000, A054060.
%K A024832 nonn
%O A024832 2,1
%A A024832 _Clark Kimberling_