A383229 Indices of record low-water marks of the sequence abs((sin n)^n).

0, 1, 2, 3, 6, 9, 13, 16, 19, 22, 44, 66, 88, 110, 132, 154, 176, 179, 198, 201, 223, 245, 267, 289, 311, 333, 355, 710, 1065, 1420, 1775, 2130, 2485, 2840, 3195, 3550, 3905, 4260, 4615, 4970, 5325, 5680, 6035, 6390, 6745, 7100, 7455, 7810, 8165, 8520, 8875, 9230, 9585, 9940

Offset

0,3

Comments

(sin 0) ^ 0 is interpreted as limit of (sin(x)) ^ x as x -> 0.

Links

Jwalin Bhatt, Table of n, a(n) for n = 0..428

Example

The first few values of abs((sin n)^n) are:
  abs(sin(0)^0) = 1
  abs(sin(1)^1) = 0.841470984807896
  abs(sin(2)^2) = 0.826821810431805
  abs(sin(3)^3) = 0.002810384734461
  abs(sin(4)^4) = 0.328042581863883
  abs(sin(5)^5) = 0.810814606094671
  abs(sin(6)^6) = 0.000475886020687
  abs(sin(7)^7) = 0.052831820502919
and the record low points are at n = 0, 1, 2, 3, 6, ...

Mathematica

Module[{x, y, runningMin = 1.1, positions = {0}},
  x = Range[10^6]; y = Abs[Sin[x]^x];
  Do[If[y[[i]] < runningMin, runningMin = y[[i]]; AppendTo[positions, i]; ], {i, Length[y]}];
  positions
]

Prog

(Python)
from mpmath import iv
running_min, A383229 = 2, []
for i in range(1066):
    while True:
        x = abs(iv.sin(i)**i)
        if (comparison:=x<running_min) is None:
            iv.dps += 1
            running_min = abs(iv.sin(A383229[-1])**A383229[-1])
        else: break
    if comparison:
        A383229.append(i)
        running_min = x
print(A383229)  # Jwalin Bhatt, Jan 08 2026

Crossrefs

Cf. A382815, A383283.

Sequence in context: A285084 A390789 A248187 * A190772 A130673 A385727

Adjacent sequences: A383226 A383227 A383228 * A383230 A383231 A383232

Keyword

nonn

Author

Jwalin Bhatt, Apr 28 2025

Status

approved