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.

A333521 Decimal expansion of the continued fraction expansion [2; 1, 3, 4, 7, 11, ...] (the Lucas numbers, A000032).

Original entry on oeis.org

2, 7, 6, 4, 2, 3, 3, 5, 4, 7, 2, 4, 5, 6, 0, 0, 7, 9, 2, 9, 8, 5, 4, 6, 2, 4, 9, 3, 6, 0, 4, 6, 2, 1, 0, 8, 4, 2, 3, 1, 1, 0, 1, 8, 2, 6, 6, 7, 4, 3, 4, 6, 5, 7, 3, 9, 7, 8, 0, 1, 1, 4, 6, 5, 4, 7, 7, 5, 2, 6, 5, 4, 0, 5, 5, 8, 8, 5, 1, 5, 1, 6, 9, 1, 1, 8, 8, 5, 7
Offset: 1

Views

Author

Daniel Hoyt, Mar 26 2020

Keywords

Examples

			2.764233547245600792985462493604...

Crossrefs

Cf. A073822, A000032.

A119801 Decimal representation of continued fraction 1, 1, 2, 3, 5, 8, 13 ... (Fibonacci[n]).

Original entry on oeis.org

1, 6, 9, 8, 1, 5, 6, 2, 7, 8, 8, 9, 7, 2, 2, 8, 4, 4, 6, 6, 9, 3, 1, 5, 4, 0, 4, 3, 6, 6, 8, 9, 3, 3, 6, 8, 3, 8, 2, 9, 4, 8, 6, 4, 4, 9, 3, 6, 4, 3, 7, 6, 6, 2, 2, 6, 7, 5, 0, 1, 9, 6, 5, 7, 5, 6, 8, 5, 0, 6, 8, 0, 3, 5, 7, 1, 7, 0, 2, 4, 0, 8, 5, 8, 3, 2, 6, 2, 3, 4, 3, 3, 9, 4, 7, 4, 4, 8, 2, 0, 2, 0, 9, 6, 7
Offset: 1

Views

Author

Alexander Adamchuk, Jul 30 2006

Keywords

Comments

C = 1.6981562788972284466931540436689336838294864493643766226750196575685068035717\
02408583262343394744820209675493364365510752097635919...
C is a limit of A026822[n]/A071895[n+1] = {1, 2, 5/3, 17/10, 90/53, 737/434, 9671/5695, 203828/120029, 6939823/4086681, ...} = (1 + 1/(1 + 1/(2 + 1/(3 + 1/(5 + 1/(8 + 1/(13 + 1/(21 + 1/(34 + 1/(55 + ...

Crossrefs

Cf. A026822, A071895, A000045.
Cf. A073822 (reciprocal).

Programs

  • Mathematica
    RealDigits[ Normal[ ContinuedFractionForm[ Table[ Fibonacci[k],{k,1,30}] ]], 10, 130] [[1]]

Formula

a(n) = limit[ A026822[n]/A071895[n+1], n->Infinity].

Extensions

Definition corrected by T. D. Noe, May 19 2007

A261827 Decimal expansion of the number whose continued fraction expansion consists of the perfect numbers (A000396).

Original entry on oeis.org

6, 0, 3, 5, 7, 1, 1, 7, 1, 4, 3, 0, 6, 9, 2, 3, 3, 3, 4, 6, 2, 8, 3, 9, 9, 0, 5, 2, 9, 2, 6, 0, 9, 4, 6, 1, 8, 0, 8, 0, 6, 1, 7, 5, 7, 4, 8, 1, 3, 6, 8, 9, 5, 4, 6, 1, 0, 7, 0, 6, 6, 8, 5, 6, 8, 3, 6, 0, 6, 9, 2, 0, 3, 4, 8, 2, 2, 1, 1, 6, 6, 9, 3, 7, 3, 9, 5, 4, 6, 8, 6, 6, 3, 3, 3, 4, 2, 3, 3, 0, 5, 4, 4, 2, 5
Offset: 1

Views

Author

Ilya Gutkovskiy, Sep 02 2015

Keywords

Examples

			6.0357117143069233346283990529260946180806175748136895461...

Links

Crossrefs

Cf. A000396, A073821, A073822, A073823, A073824, A052119, A064442.

Programs

  • Mathematica
    ind = {1, 2, 3, 4, 6, 7, 8, 11, 18, 24, 28, 31, 98, 111} (* from A016027 *); p = Prime@ ind; pn = (2^p - 1)(2^(p - 1)); RealDigits[ FromContinuedFraction@ pn, 10, 111][[1]] (* Robert G. Wilson v, Sep 13 2015 *)

A333567 Decimal expansion of the continued fraction expansion [1; 3, 4, 7, 11, 18,...] (the Lucas numbers beginning at 1, A000204).

Original entry on oeis.org

1, 3, 0, 8, 5, 0, 0, 5, 2, 7, 8, 8, 7, 2, 3, 1, 3, 5, 2, 7, 5, 9, 4, 9, 8, 3, 9, 9, 7, 4, 8, 1, 0, 9, 6, 8, 0, 7, 3, 4, 6, 0, 7, 9, 8, 6, 2, 6, 7, 9, 8, 5, 8, 8, 9, 9, 9, 9, 9, 1, 2, 7, 4, 9, 7, 7, 9, 7, 3, 2, 7, 9, 6, 3, 4, 0, 8, 7, 9, 6, 6, 7, 2, 1, 2, 3, 3, 3, 7
Offset: 1

Views

Author

Daniel Hoyt, Mar 26 2020

Keywords

Examples

			1.3085005278872313527594983997481096807346079862679858899999...

Crossrefs

Cf. A000204, A333521, A073822.

Programs

  • Mathematica
    RealDigits[FromContinuedFraction[LucasL[Range[20]]],10,120][[1]] (* Harvey P. Dale, Jun 06 2021 *)

Formula

Equals 1/(A333521 - 2).
Showing 1-4 of 4 results.

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