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 1-3 of 3 results.

A190297 Bisection of A013697.

Original entry on oeis.org

1, 12, 57, 245, 1005, 4063, 16327, 65435, 261965, 1048259, 4193742, 16776218, 67107091, 268432305, 1073736223, 4294957340, 17179851485, 68719445272, 274877851009, 1099511528337, 4398046334325, 17592185730143, 70368743618958, 281474975717403, 1125899905076842
Offset: 1

Views

Author

N. J. A. Sloane, May 13 2011

Keywords

Formula

a(n) = floor(1/(zeta(2n)-1)).

A190584 Bisection of A013697.

Original entry on oeis.org

4, 27, 119, 497, 2023, 8149, 32692, 130938, 524050, 2096730, 8387859, 33553102, 134215364, 536866711, 2147476180, 8589921317, 34359714770, 137438911520, 549755739309, 2199023122967, 8796092786503, 35184371669802, 140737487610388, 562949952096975
Offset: 1

Views

Author

N. J. A. Sloane, May 13 2011

Keywords

Formula

a(n) = floor(1/(zeta(2n+1)-1)).

A343244 Position of the first occurrence of an element in the continued fraction of zeta(n) which is larger than the second element.

Original entry on oeis.org

5, 4, 8, 14, 10, 63, 120, 79, 1270, 779, 1749, 3410, 13668, 17704, 20909, 175782, 127426
Offset: 2

Views

Author

Amiram Eldar, Apr 08 2021

Keywords

Comments

a(20) = 111604.
The corresponding values of the a(n)-th elements are 4, 18, 183, 32, 61, 9283, 462, 1483, 3530, 3484, 10812, 8954, ...

Examples

			The continued fraction of zeta(3) is [1; 4, 1, 18, 1, 1, ...]. The first element which is larger than 4 is 18 whose position is 4. Therefore, a(3) = 4.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Module[{c = ContinuedFraction[Zeta[n], 10000]}, FirstPosition[c, _?(# > c[[2]] &)][[1]]]; Array[a, 10, 2]
Showing 1-3 of 3 results.