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.

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A234362 Floor(AGM(n^2, n^3)), where AGM denotes the arithmetic-geometric mean.

Original entry on oeis.org

0, 1, 5, 16, 35, 65, 106, 161, 231, 318, 425, 551, 700, 872, 1069, 1293, 1545, 1827, 2140, 2486, 2866, 3281, 3734, 4225, 4755, 5327, 5942, 6601, 7306, 8057, 8856, 9706, 10606, 11558, 12565, 13626, 14744, 15919, 17154, 18449, 19805, 21225, 22709, 24259, 25876, 27561
Offset: 0

Views

Author

Alex Ratushnyak, Dec 24 2013

Keywords

Crossrefs

Programs

  • Python
    import math
    for n in range(67):
      x = n*n
      y = x*n
      a = (x+y)*0.5
      g = math.sqrt(x*y)
      while abs(a-g)>0.00000000001:
        x = a
        y = g
        a = (x+y)*0.5
        g = math.sqrt(x*y)
      print(int(a), end=', ')

A234369 Floor(AGM(1, triangular(n))), where AGM denotes the arithmetic-geometric mean.

Original entry on oeis.org

0, 1, 1, 2, 4, 5, 7, 9, 11, 13, 16, 18, 21, 24, 27, 30, 33, 37, 41, 44, 48, 53, 57, 61, 66, 71, 76, 81, 86, 91, 97, 102, 108, 114, 120, 126, 132, 139, 145, 152, 159, 166, 173, 180, 187, 195, 202, 210, 218, 226, 234, 242, 251, 259, 268, 277, 286, 295, 304, 313, 323, 332
Offset: 0

Views

Author

Alex Ratushnyak, Dec 25 2013

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Floor[ArithmeticGeometricMean[1, n*(n+1)/2]], {n, 0, 100}] (* Vaclav Kotesovec, May 09 2016 *)
    Floor[ArithmeticGeometricMean[1,#]]&/@Accumulate[Range[0,100]] (* Harvey P. Dale, Nov 01 2022 *)

Formula

a(n) ~ Pi*n^2/(8*log(n) + 4*log(2)). - Vaclav Kotesovec, May 09 2016
Showing 1-2 of 2 results.