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

0, 1, 2, 5, 8, 11, 33, 55, 77, 99, 121, 143, 165, 187, 190, 209, 212, 234, 256, 278, 300, 322, 344, 366, 633, 655, 677, 699, 721, 1032, 1054, 1076, 1387, 1409, 1431, 1764, 2119, 2474, 2829, 3184, 3539, 3894, 4249, 4604, 4959, 5314, 5669, 6024, 6379, 6734, 7089, 7444, 7799, 8154, 8509, 8864, 9219, 9574, 9929, 10284

Offset: 0

Author

Jwalin Bhatt, Apr 28 2025

Keywords

• nonn

Examples

			The first few values of abs((cos n)^n) are:
abs(cos(0)^0) = 1
abs(cos(1)^1) = 0.540302305868139
abs(cos(2)^2) = 0.173178189568194
abs(cos(3)^3) = 0.970276937921503
abs(cos(4)^4) = 0.182542548055270
abs(cos(5)^5) = 0.001836568887601
abs(cos(6)^6) = 0.783591241730686
abs(cos(7)^7) = 0.138422055397017
abs(cos(8)^8) = 0.000000200865224
abs(cos(9)^9) = 0.432737211396127
and the record low points are at n = 0, 1, 2, 5, 8, ...
		

Crossrefs

C.f. A382564, A383229.

Programs

Mathematica

Module[{x, y, runningMin = 1.1, positions = {}},
  x = Range[0,10^6];y = Abs[Cos[x]^x];
  Do[If[y[[i]] < runningMin,runningMin = y[[i]];AppendTo[positions, i-1];],{i, Length[y]}];
  positions
]