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

%I A383229 #30 May 01 2025 08:31:16
%S A383229 0,1,2,3,6,9,13,16,19,22,44,66,88,110,132,154,176,179,198,201,223,245,
%T A383229 267,289,311,333,355,710,1065,1420,1775,2130,2485,2840,3195,3550,3905,
%U A383229 4260,4615,4970,5325,5680,6035,6390,6745,7100,7455,7810,8165,8520,8875,9230,9585,9940
%N A383229 Indices of record low-water marks of the sequence abs((sin n)^n).
%C A383229 (sin 0) ^ 0 is interpreted as limit of (sin(x)) ^ x as x -> 0.
%H A383229 Jwalin Bhatt, <a href="/A383229/b383229.txt">Table of n, a(n) for n = 0..428</a>
%e A383229 The first few values of abs((sin n)^n) are:
%e A383229 abs(sin(0)^0) = 1
%e A383229 abs(sin(1)^1) = 0.841470984807896
%e A383229 abs(sin(2)^2) = 0.826821810431805
%e A383229 abs(sin(3)^3) = 0.002810384734461
%e A383229 abs(sin(4)^4) = 0.328042581863883
%e A383229 abs(sin(5)^5) = 0.810814606094671
%e A383229 abs(sin(6)^6) = 0.000475886020687
%e A383229 abs(sin(7)^7) = 0.052831820502919
%e A383229 and the record low points are at n = 0, 1, 2, 3, 6, ...
%t A383229 Module[{x, y, runningMin = 1.1, positions = {0}},
%t A383229   x = Range[10^6];y = Abs[Sin[x]^x];
%t A383229   Do[If[y[[i]] < runningMin,runningMin = y[[i]];AppendTo[positions, i];],{i, Length[y]}];
%t A383229   positions
%t A383229 ]
%o A383229 (Python)
%o A383229 from mpmath import mp
%o A383229 A383229, min_val = [0], 1
%o A383229 for i in range(1, 1+10**5):
%o A383229     if (current_val:=abs(mp.sin(i)**i)) < min_val:
%o A383229         min_val = current_val
%o A383229         A383229.append(i)
%Y A383229 Cf. A382815, A383283.
%K A383229 nonn
%O A383229 0,3
%A A383229 _Jwalin Bhatt_, Apr 28 2025