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.
%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