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URL: https://oeis.org/A383540

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A383540
Positive numbers k such that (sin k)^k sets a new record.
3
1, 8, 33, 48269, 48624, 48979, 49334, 49689, 50044, 50399, 50754, 51109, 51464, 51819, 52174, 573204, 37362253, 42781604
OFFSET
1,2
EXAMPLE
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, ...
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
]
PROG
(Python)
from mpmath import iv
running_max, A383540 = 0, []
for i in range(1, 52175):
while True:
x = iv.sin(i)**i
if (comparison:=x>running_max) is None:
iv.dps += 1
running_max = iv.sin(A383540[-1])**A383540[-1]
else: break
if comparison:
A383540.append(i)
running_max = x
print(A383540) # Jwalin Bhatt, Jan 23 2026
CROSSREFS
Sequence in context: A204191 A041118 A308879 * A297904 A298498 A091720
KEYWORD
nonn,more
AUTHOR
Jwalin Bhatt, Apr 29 2025
STATUS
approved