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 1-4 of 4 results.

A090852 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 1 is equal to n.

Original entry on oeis.org

1, 4, 7, 10, 13, 16, 20, 24, 27, 31, 35, 39, 43, 47, 51, 55, 60, 64, 68, 73, 77, 81, 86, 90, 95, 100, 104, 109, 113, 118, 123, 127, 132, 137, 142, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241, 246, 251, 256, 262
Offset: 1

Views

Author

Paul D. Hanna, Dec 10 2003

Keywords

Links

Crossrefs

Cf. A090853, A090854.

Programs

  • Mathematica
    Table[Ceiling[y /. FindRoot[Pi/(2*EllipticK[1 - y^2]) == n, {y, 2*n}]], {n, 1, 60}] (* Vaclav Kotesovec, Sep 28 2019 *)

Formula

floor( agm(a(n), 1) ) = n, for n>=1.

A090855 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 1 is equal to 2^n.

Original entry on oeis.org

1, 4, 10, 24, 55, 127, 288, 640, 1408, 3069, 6642, 14281, 30544, 65028, 137896, 291399, 613885, 1289715, 2702909, 5652038, 11795170, 24570079, 51095155, 106092067, 219972452, 455493427, 942031726, 1946056082, 4015916211
Offset: 0

Views

Author

Paul D. Hanna, Dec 10 2003

Keywords

Crossrefs

Cf. A090852, A090854, A090856.

Programs

  • Mathematica
    Flatten[{1, Table[Ceiling[y /. FindRoot[Log[Pi/(2*EllipticK[1 - y^2])] == n*Log[2], {y, n*2^n}, MaxIterations -> 1000]], {n, 1, 50}]}] (* Vaclav Kotesovec, Sep 28 2019 *)

Formula

floor( agm(a(n), 1) ) = 2^n, for n>=0.

A090853 a(n) is the least positive integer such that the arithmetic-geometric mean satisfies: floor( agm(a(n),a(n-2)) ) = a(n-1) for n>2, with a(1)=1, a(2)=2.

Original entry on oeis.org

1, 2, 4, 7, 12, 19, 28, 40, 55, 73, 94, 118, 145, 176, 211, 250, 293, 340, 391, 446, 505, 568, 635, 706, 781, 860, 943, 1030, 1121, 1216, 1315, 1418, 1525, 1637, 1754, 1876, 2003, 2135, 2272, 2414, 2561, 2713, 2870, 3032, 3199, 3371, 3548, 3730, 3917, 4109
Offset: 1

Views

Author

Paul D. Hanna, Dec 10 2003

Keywords

Crossrefs

Cf. A090852, A090854, A090855.

A090856 a(n) is the least positive integer such that the integer part of the arithmetic-geometric mean of a(n) and 1 is equal to 3^n.

Original entry on oeis.org

1, 7, 27, 104, 378, 1327, 4553, 15351, 51072, 168147, 548915, 1779377, 5734022, 18384612, 58688163, 186632570, 591509670, 1869118923, 5890466415, 18518945789, 58094637801, 181884111404, 568416743474, 1773443888599
Offset: 0

Views

Author

Paul D. Hanna, Dec 10 2003

Keywords

Crossrefs

Cf. A090852, A090854, A090857.

Formula

floor( agm(a(n), 1) ) = 3^n, for n>=0.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.