cp's OEIS Frontend

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

%I A382815 #59 May 07 2025 10:38:29
%S A382815 1,8,11,51464,51819,52174,573204,37362253,42781604,122925461,
%T A382815 534483448,3083975227
%N A382815 Positive numbers k such that abs((sin k)^k) sets a new record.
%H A382815 David Consiglio, Jr., <a href="/A382815/a382815.py.txt">Python using high precision math</a>
%e A382815 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
%t A382815 Module[{x, y, runningMax = 0, positions = {}},
%t A382815   x = Range[1, 10^6];y = Abs[Sin[x]^x];
%t A382815   Do[If[y[[i]] > runningMax,runningMax = y[[i]];AppendTo[positions, i];],{i, Length[y]}];
%t A382815   positions
%t A382815 ]
%o A382815 (Python)
%o A382815 import numpy as np, pandas as pd
%o A382815 x = np.arange(1, 1+10**8)
%o A382815 y = pd.Series(abs(np.sin(x) ** x))
%o A382815 A382815 = sorted([1+int(np.where(y==m)[0][0]) for m in set(y.cummax())])
%Y A382815 Cf. A004112 (analog for |sin n|), A383540.
%K A382815 nonn,more
%O A382815 1,2
%A A382815 _Jwalin Bhatt_, Apr 28 2025
%E A382815 a(10)-a(12) from _David Consiglio, Jr._, Apr 28 2025
%E A382815 Definition clarified by _Jakub Buczak_, May 07 2025