1,2

David Consiglio, Jr., Python using high precision math

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

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)

from mpmath import iv

running_max, A382815 = 0, []

for i in range(1, 52175):

while True:

x = abs(iv.sin(i)**i)

if (comparison:=x>running_max) is None:

iv.dps += 1

running_max = abs(iv.sin(A382815[-1])**A382815[-1])

else: break

if comparison:

A382815.append(i)

running_max = x

print(A382815) # Jwalin Bhatt, Jan 19 2026

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

Sequence in context: A074042 A140478 A111021 * A126814 A172391 A227239

Adjacent sequences: A382812 A382813 A382814 * A382816 A382817 A382818

nonn,more

Jwalin Bhatt, Apr 28 2025

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

Definition clarified by Jakub Buczak, May 07 2025

approved