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

1, 8, 33, 48269, 48624, 48979, 49334, 49689, 50044, 50399, 50754, 51109, 51464, 51819, 52174, 573204, 37362253, 42781604

Offset: 1

Author

Jwalin Bhatt, Apr 29 2025

Keywords

• nonn
• more

Examples

			The first few values of (sin k)^k, k >= 1, are:
sin(1)^1   =  0.841470984807896
sin(2)^2   =  0.826821810431805
sin(3)^3   =  0.002810384734461
sin(4)^4   =  0.328042581863883
sin(5)^5   = -0.81081460609467
sin(6)^6   =  0.000475886020687
sin(7)^7   =  0.052831820502919
sin(8)^8   =  0.917970288581835
sin(9)^9   =  0.000342924768404
sin(10)^10 =  0.002270688337734
sin(11)^11 = -0.99989227733272
and the record high points are at k = 1, 8, 33, ...
		

Crossrefs

Cf. A382815, A383541.

Programs

Mathematica

Module[{x, y, runningMax = 0, positions = {}},
  x = Range[1, 10^6]; y = Sin[x]^x;
  Do[If[y[[i]] > runningMax, runningMax = y[[i]]; AppendTo[positions, i]; ], {i, Length[y]}];
  positions
]

Python

import numpy as np, pandas as pd
x = np.arange(1, 1+10**8)
y = pd.Series(np.sin(x) ** x)
A383540 = sorted([1+int(np.where(y==m)[0][0]) for m in set(y.cummax())])