A382564 Indices of records of the sequence abs((cos n)^n) starting from n = 1.
1, 3, 22, 355, 5419351, 411557987, 1068966896, 2549491779
Offset: 1
Examples
The first few values of abs((cos n)^n), n >= 1, are: abs(cos(1)^1) = 0.5403023058 abs(cos(2)^2) = 0.1731781895 abs(cos(3)^3) = 0.9702769379 abs(cos(4)^4) = 0.1825425480 abs(cos(5)^5) = 0.0018365688 and the record high points are at n = 1, 3, 22, ...
Programs
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Mathematica
Module[{x, y, runningMax = 0, positions = {}}, x = Range[10^6]; y = Abs[Cos[x]^x]; Do[If[y[[i]] > runningMax, runningMax = y[[i]]; AppendTo[positions, i]; ], {i, Length[y]}]; positions ] -
Python
import numpy as np x = np.arange(1, 1+10**8) y = abs(np.cos(x) ** x) A382564 = sorted([1+int(np.where(y==m)[0][0]) for m in set(np.maximum.accumulate(y))])
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Python
from mpmath import mp mp.dps = 1 running_max, A382564 = 0, [] for n in range(1, 1+10**5): while ((y:=abs(mp.cos(n)**n)) == 1): mp.dps += 1 if y > running_max: running_max = y A382564.append(n)
Extensions
a(6)-a(8) from Jakub Buczak, May 04 2025
Comments