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Least k such that Sum_{i=1..k} cos(1/sqrt(i)) > n.
0

%I #9 Oct 01 2024 20:13:26

%S 1,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,

%T 28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,

%U 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74

%N Least k such that Sum_{i=1..k} cos(1/sqrt(i)) > n.

%C The complement of this sequence is 2, 6, 36, and 260, for all values up to 1000.

%C For n > 0, these values are actually k + 1. - _Sean A. Irvine_, Oct 01 2024

%t f[n_] := Block[{k = 1, s = 0}, While[s < n, s = s + Cos[1/Sqrt[k]]; k++ ]; k]; Table[ f[n], {n, 0, 60} ]

%K nonn

%O 0,2

%A _Robert G. Wilson v_, Aug 01 2002