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.

A010484 Decimal expansion of square root of 29.

Original entry on oeis.org

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

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Author

N. J. A. Sloane

Keywords

Comments

Continued fraction expansion is 5 followed by {2, 1, 1, 2, 10} repeated. - Harry J. Smith, Jun 04 2009
The fundamental algebraic (integer) number in the field Q(sqrt(29)) is (1 + sqrt(29))/2 = A223140. - Wolfdieter Lang, Nov 21 2023

Examples

			5.385164807134504031250710491540329556295120161644788837680388670016645....

Links

Crossrefs

Cf. A010128 (continued fraction). - Harry J. Smith, Jun 04 2009
Cf. A010128.

Programs

  • Mathematica
    RealDigits[N[Sqrt[29], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)
  • PARI
    default(realprecision, 20080); x=sqrt(29); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010484.txt", n, " ", d));  \\ Harry J. Smith, Jun 04 2009

A041046 Numerators of continued fraction convergents to sqrt(29).

Original entry on oeis.org

5, 11, 16, 27, 70, 727, 1524, 2251, 3775, 9801, 101785, 213371, 315156, 528527, 1372210, 14250627, 29873464, 44124091, 73997555, 192119201, 1995189565, 4182498331, 6177687896, 10360186227, 26898060350
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

From Johannes W. Meijer, Jun 12 2010: (Start)
The terms of this sequence can be constructed with the terms of sequence A087130.
For the terms of the periodical sequence of the continued fraction for sqrt(29) see A010128. We observe that its period is five. The decimal expansion of sqrt(29) is A010484. (End)

Links

Crossrefs

Cf. A041047, A041018, A041046, A041090, A041150, A041226, A041318, A041426, A041550, A010484.

Programs

  • Mathematica
    Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[29],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Numerator[Convergents[Sqrt[29], 30]] (* Vincenzo Librandi, Oct 28 2013 *)
LinearRecurrence[ {0,0,0,0,140,0,0,0,0,1},{5,11,16,27,70,727,1524,2251,3775,9801},30] (* Harvey P. Dale, Jun 10 2021 *)

Formula

a(5*n) = A087130(3*n+1), a(5*n+1) = (A087130(3*n+2) - A087130(3*n+1))/2, a(5*n+2) = ( A087130(3*n+2) + A087130(3*n+1))/2, a(5*n+3) = A087130(3*n+2) and a(5*n+4) = A087130(3*n+3)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: (5 + 11*x + 16*x^2 + 27*x^3 + 70*x^4 + 27*x^5 - 16*x^6 + 11*x^7 - 5*x^8 + x^9)/(1 - 140*x^5 - x^10) - Peter J. C. Moses, Jul 29 2013

A041047 Denominators of continued fraction convergents to sqrt(29).

Original entry on oeis.org

1, 2, 3, 5, 13, 135, 283, 418, 701, 1820, 18901, 39622, 58523, 98145, 254813, 2646275, 5547363, 8193638, 13741001, 35675640, 370497401, 776670442, 1147167843, 1923838285, 4994844413, 51872282415
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

The terms of this sequence can be constructed with the terms of sequence A052918.
For the terms of the periodical sequence of the continued fraction for sqrt(29) see A010128. We observe that its period is five. The decimal expansion of sqrt(29) is A010484. - Johannes W. Meijer, Jun 12 2010

Links

Crossrefs

Cf. A041046.
Cf. A041019, A041047, A041091, A041151, A041227, A041319, A041427, A041551.

Programs

  • Magma
    I:=[1, 2, 3, 5, 13, 135, 283, 418, 701, 1820]; [n le 10 select I[n] else 140*Self(n-5)+Self(n-10): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013
  • Mathematica
    Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[29],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Denominator[Convergents[Sqrt[29], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

Formula

a(5*n) = A052918(3*n), a(5*n+1) = (A052918(3*n+1) - A052918(3*n))/2, a(5*n+2) = (A052918(3*n+1) + A052918(3*n))/2, a(5*n+3) = A052918(3*n+1) and a(5*n+4) = A052918(3*n+2)/2. - Johannes W. Meijer, Jun 12 2010
G.f.: (1 + 2*x + 3*x^2 + 5*x^3 + 13*x^4 - 5*x^5 + 3*x^6 - 2*x^7 + x^8)/(1 - 140*x^5 - x^10). - Peter J. C. Moses, Jul 29 2013
a(n) = 140*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 10 2013
Showing 1-3 of 3 results.

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

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