A382815 Positive numbers k such that abs((sin k)^k) sets a new record.

1, 8, 11, 51464, 51819, 52174, 573204, 37362253, 42781604, 122925461, 534483448, 3083975227

Offset: 1

Author

Jwalin Bhatt, Apr 28 2025

Keywords

• nonn
• more

Examples

			The first few values of abs((sin k)^n), k >= 1, are 0.8414709848, 0.8268218104, 0.002810384737, 0.3280425818, 0.8108146063, 0.0004758860207, 0.05283182049, 0.9179702884, 0.0003429247681, 0.002270688338, 0.9998922779, 0.0005695672234, ... and the record high points are at k = 1, 8, 11, ... - _N. J. A. Sloane_, Apr 28 2025
		

Links

• David Consiglio, Jr., Python using high precision math

Crossrefs

Cf. A004112 (analog for |sin n|), A383540.

Programs

Mathematica

Module[{x, y, runningMax = 0, positions = {}},
  x = Range[1, 10^6];y = Abs[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(abs(np.sin(x) ** x))
A382815 = sorted([1+int(np.where(y==m)[0][0]) for m in set(y.cummax())])

Extensions

a(10)-a(12) from David Consiglio, Jr., Apr 28 2025

Definition clarified by Jakub Buczak, May 07 2025