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.

A054781 First position of n in continued fraction for Khinchin's constant.

Original entry on oeis.org

2, 1, 10, 47, 4, 34, 76, 65, 119, 11, 104, 27, 103, 110, 675, 80, 1080, 146, 142, 369, 246, 586, 679, 16, 1428, 1621, 1021, 1627, 64, 1342, 799, 157, 409, 506, 1406, 1783, 1445, 206, 3160, 300, 2683, 2037, 4207, 5204, 271, 523, 368, 7892, 2255, 72, 970
Offset: 1

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Author

Hans Havermann, May 27 2000

Keywords

Comments

Indexing of the terms is based on writing a c.f. as [a_1; a_2, a_3, ...]; the more standard convention of [a_0; a_1, a_2, ...] requires subtracting 1 from each term of the sequence.
Smallest positive integers not occurring in the first 106621 terms of the c.f. are 236, 260, 265, 279, 282, 290, 294, 297, 299, ... - Eric W. Weisstein, Oct 01 2011

Links

Crossrefs

Cf. A224851 (= a(n) - 1).
Cf. A002211, A054866, A054870.

Formula

a(n) = A224851(n) + 1.

A054866 Incrementally largest terms in the continued fraction for Khinchin's constant.

Original entry on oeis.org

2, 5, 10, 24, 90, 770, 941, 11759, 54097, 231973
Offset: 1

Views

Author

Hans Havermann, May 27 2000

Keywords

Comments

No other high water marks in the first 106621 terms of the c.f. - Eric W. Weisstein, Oct 01 2011

Links

Crossrefs

Cf. A002211, A054781, A054870.

Programs

  • Mathematica
    DeleteDuplicates[ContinuedFraction[Khinchin,10000],GreaterEqual] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Sep 11 2024 *)

A224852 Positions of the incrementally largest terms in the continued fraction for Khinchin's constant.

Original entry on oeis.org

0, 3, 10, 15, 23, 104, 1701, 2445, 18995, 60037
Offset: 0

Views

Author

Eric W. Weisstein, Jul 22 2013

Keywords

Comments

Same as A054870 except correctly indexed with [a_0; a_1, a_2, ...]

Links

Crossrefs

Cf. A054870 (= a(n) + 1).
Cf. A054866 (incrementally largest terms).
Cf. A002211 (continued fraction of Khinchin's constant).

Programs

  • Mathematica
    Module[{nn=2500,k},k=ContinuedFraction[Khinchin,nn];DeleteDuplicates[Thread[{Range[nn],k}],GreaterEqual[#1[[2]],#2[[2]]]&]][[;;,1]]-1 (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Feb 28 2025 *)

Formula

a(n) = A054870(n) - 1.
Showing 1-3 of 3 results.

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

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