cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A382815 Positive numbers k such that abs((sin k)^k) sets a new record.

Original entry on oeis.org

1, 8, 11, 51464, 51819, 52174, 573204, 37362253, 42781604, 122925461, 534483448, 3083975227
Offset: 1

Views

Author

Jwalin Bhatt, Apr 28 2025

Keywords

Examples

			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
		

Crossrefs

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

Programs

  • Mathematica
    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
    import numpy as np, pandas as pd
    x = np.arange(1, 1+10**8)
    y = pd.Series(abs(np.sin(x) ** x))
    A382815 = sorted([1+int(np.where(y==m)[0][0]) for m in set(y.cummax())])

Extensions

a(10)-a(12) from David Consiglio, Jr., Apr 28 2025
Definition clarified by Jakub Buczak, May 07 2025

A383541 Positive numbers k such that (cos k)^k sets a new record.

Original entry on oeis.org

1, 6, 19, 22, 710, 1146408, 10838702, 80143857, 245850922, 411557987, 1068966896
Offset: 1

Views

Author

Jwalin Bhatt, Apr 29 2025

Keywords

Examples

			The first few values of (cos k)^k, k >= 1, are:
  cos(1)^1 =  0.540302305868139
  cos(2)^2 =  0.173178189568194
  cos(3)^3 = -0.97027693792150
  cos(4)^4 =  0.182542548055270
  cos(5)^5 =  0.001836568887601
  cos(6)^6 =  0.783591241730686
  cos(7)^7 =  0.138422055397017
  cos(8)^8 =  0.000000200865224
  cos(9)^9 = -0.43273721139612
and the record high points are at k = 1, 6, 19, ...
		

Crossrefs

Programs

  • Mathematica
    Module[{x, y, runningMax = 0, positions = {}},
      x = Range[1, 10^6]; y = Cos[x]^x;
      Do[If[y[[i]] > runningMax, runningMax = y[[i]]; AppendTo[positions, i]; ], {i, Length[y]}];
      positions
    ]
  • Python
    import numpy as np
    x = np.arange(1, 1+10**8)
    y = np.cos(x) ** x
    A383541 = sorted([1+int(np.where(y==m)[0][0]) for m in set(np.maximum.accumulate(y))])

Formula

Conjecture: a(n) = A002485(n+7) for n >= 9. - Jakub Buczak, May 05 2025

Extensions

a(9)-a(11) from Jakub Buczak, May 05 2025
Showing 1-2 of 2 results.