cp's OEIS Frontend

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.

A383540 Positive numbers k such that (sin k)^k sets a new record.

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%I A383540 #13 May 12 2025 16:22:21
%S A383540 1,8,33,48269,48624,48979,49334,49689,50044,50399,50754,51109,51464,
%T A383540 51819,52174,573204,37362253,42781604
%N A383540 Positive numbers k such that (sin k)^k sets a new record.
%e A383540 The first few values of (sin k)^k, k >= 1, are:
%e A383540 sin(1)^1   =  0.841470984807896
%e A383540 sin(2)^2   =  0.826821810431805
%e A383540 sin(3)^3   =  0.002810384734461
%e A383540 sin(4)^4   =  0.328042581863883
%e A383540 sin(5)^5   = -0.81081460609467
%e A383540 sin(6)^6   =  0.000475886020687
%e A383540 sin(7)^7   =  0.052831820502919
%e A383540 sin(8)^8   =  0.917970288581835
%e A383540 sin(9)^9   =  0.000342924768404
%e A383540 sin(10)^10 =  0.002270688337734
%e A383540 sin(11)^11 = -0.99989227733272
%e A383540 and the record high points are at k = 1, 8, 33, ...
%t A383540 Module[{x, y, runningMax = 0, positions = {}},
%t A383540   x = Range[1, 10^6]; y = Sin[x]^x;
%t A383540   Do[If[y[[i]] > runningMax, runningMax = y[[i]]; AppendTo[positions, i]; ], {i, Length[y]}];
%t A383540   positions
%t A383540 ]
%o A383540 (Python)
%o A383540 import numpy as np, pandas as pd
%o A383540 x = np.arange(1, 1+10**8)
%o A383540 y = pd.Series(np.sin(x) ** x)
%o A383540 A383540 = sorted([1+int(np.where(y==m)[0][0]) for m in set(y.cummax())])
%Y A383540 Cf. A382815, A383541.
%K A383540 nonn,more
%O A383540 1,2
%A A383540 _Jwalin Bhatt_, Apr 29 2025