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.

A248281 Egyptian fraction representation of sqrt(56) (A010509) using a greedy function.

Original entry on oeis.org

7, 3, 7, 141, 31154, 5919757544, 160210422116327440975, 51936028072305364257094751268091425897982, 4468374619865723526161303689130955516769923438522458566697540434310939905017570043
Offset: 0

Views

Author

Robert G. Wilson v, Oct 04 2014

Keywords

Crossrefs

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.
Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Programs

  • Mathematica
    Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[ iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 56]]

A040048 Continued fraction for sqrt(56).

Original entry on oeis.org

7, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			7.4833147735478827711674974... = 7 + 1/(2 + 1/(14 + 1/(2 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 06 2009

Links

Crossrefs

Cf. A010509 Decimal expansion. - Harry J. Smith, Jun 06 2009

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[56],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 30000); x=contfrac(sqrt(56)); for (n=0, 20000, write("b040048.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

A041096 Numerators of continued fraction convergents to sqrt(56).

Original entry on oeis.org

7, 15, 217, 449, 6503, 13455, 194873, 403201, 5839687, 12082575, 174995737, 362074049, 5244032423, 10850138895, 157145976953, 325142092801, 4709135276167, 9743412645135, 141116912308057, 291977237261249, 4228798233965543, 8749573705192335, 126722830106658233
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041097, A010509.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[56], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

G.f.: -(x+1)*(x^2-8*x-7) / (x^4-30*x^2+1). - Colin Barker, Nov 04 2013

Extensions

More terms from Colin Barker, Nov 04 2013

A041097 Denominators of continued fraction convergents to sqrt(56).

Original entry on oeis.org

1, 2, 29, 60, 869, 1798, 26041, 53880, 780361, 1614602, 23384789, 48384180, 700763309, 1449910798, 20999514481, 43448939760, 629284671121, 1302018282002, 18857540619149, 39017099520300, 565096933903349, 1169210967326998, 16934050476481321, 35037311920289640
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041096, A040048, A020813, A010509.

Programs

  • Magma
    I:=[1, 2, 29, 60]; [n le 4 select I[n] else 30*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator[Convergents[Sqrt[56], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,30,0,-1},{1,2,29,60},30] (* Harvey P. Dale, Dec 09 2014 *)

Formula

G.f.: -(x^2-2*x-1) / (x^4-30*x^2+1). - Colin Barker, Nov 12 2013
a(n) = 30*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 12 2013
Showing 1-4 of 4 results.

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

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