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A383117 Indices of record high-water marks of the sequence abs((cos p)^p) where p is the numerator of the n-th convergent to Pi (A002485), starting from n = 1.

%I A383117 #52 May 07 2025 08:26:20
%S A383117 1,2,3,5,13,17,18,19,20,22,26,28,30,32,33,34,38,39,40,43,44,46,48,49,
%T A383117 50,52,53,55,59,62,65,67,70,71,72,73,75,76,77,78,80,81,83,86,88,90,91,
%U A383117 95,97,98,100,102,103,105,106,107,109,110,111,112,114,117,119,122,123,124,125,127,129
%N A383117 Indices of record high-water marks of the sequence abs((cos p)^p) where p is the numerator of the n-th convergent to Pi (A002485), starting from n = 1.
%H A383117 Jwalin Bhatt, <a href="/A383117/b383117.txt">Table of n, a(n) for n = 1..586</a>
%e A383117 The first few values of abs((cos p)^p), are:
%e A383117   | n  | p      | abs((cos p)^p)    |
%e A383117   |----|--------|-------------------|
%e A383117   | 1  | 1      | 0.540302305868139 |
%e A383117   | 2  | 3      | 0.970276937921503 |
%e A383117   | 3  | 22     | 0.999138535075440 |
%e A383117   | 4  | 333    | 0.987127208495661 |
%e A383117   | 5  | 355    | 0.999999838708950 |
%e A383117   | 6  | 103993 | 0.999980973024431 |
%e A383117   | 7  | 104348 | 0.999993669716665 |
%e A383117   | 8  | 208341 | 0.999993141212817 |
%e A383117   | 9  | 312689 | 0.999998684509338 |
%e A383117   | 10 | 833719 | 0.999997769972478 |
%e A383117 and the record high points are at n = 1, 2, 3, 5, 13, ...
%t A383117 Module[{x, y, runningMax = 0, positions = {}},
%t A383117   x = Join[{1}, Numerator @ Convergents[Pi, 64]]; y = Abs[Cos[x]^x];
%t A383117   Do[If[y[[i]] > runningMax, runningMax = y[[i]]; AppendTo[positions, i]; ], {i, Length[y]}];
%t A383117   positions
%t A383117 ]
%Y A383117 Cf. A002485, A382564.
%K A383117 nonn
%O A383117 1,2
%A A383117 _Jwalin Bhatt_, May 01 2025