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A383283 Indices of record low-water marks of the sequence abs((cos n)^n).

%I A383283 #19 Apr 29 2025 13:30:56
%S A383283 0,1,2,5,8,11,33,55,77,99,121,143,165,187,190,209,212,234,256,278,300,
%T A383283 322,344,366,633,655,677,699,721,1032,1054,1076,1387,1409,1431,1764,
%U A383283 2119,2474,2829,3184,3539,3894,4249,4604,4959,5314,5669,6024,6379,6734,7089,7444,7799,8154,8509,8864,9219,9574,9929,10284
%N A383283 Indices of record low-water marks of the sequence abs((cos n)^n).
%e A383283 The first few values of abs((cos n)^n) are:
%e A383283 abs(cos(0)^0) = 1
%e A383283 abs(cos(1)^1) = 0.540302305868139
%e A383283 abs(cos(2)^2) = 0.173178189568194
%e A383283 abs(cos(3)^3) = 0.970276937921503
%e A383283 abs(cos(4)^4) = 0.182542548055270
%e A383283 abs(cos(5)^5) = 0.001836568887601
%e A383283 abs(cos(6)^6) = 0.783591241730686
%e A383283 abs(cos(7)^7) = 0.138422055397017
%e A383283 abs(cos(8)^8) = 0.000000200865224
%e A383283 abs(cos(9)^9) = 0.432737211396127
%e A383283 and the record low points are at n = 0, 1, 2, 5, 8, ...
%t A383283 Module[{x, y, runningMin = 1.1, positions = {}},
%t A383283   x = Range[0,10^6];y = Abs[Cos[x]^x];
%t A383283   Do[If[y[[i]] < runningMin,runningMin = y[[i]];AppendTo[positions, i-1];],{i, Length[y]}];
%t A383283   positions
%t A383283 ]
%Y A383283 C.f. A382564, A383229.
%K A383283 nonn
%O A383283 0,3
%A A383283 _Jwalin Bhatt_, Apr 28 2025