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.

A248312 Egyptian fraction representation of sqrt(89) (A010540) using a greedy function.

Original entry on oeis.org

9, 3, 10, 1544, 7672861, 165539010732510, 586864529453110226492165851331, 871003380327454541280891832552137332670921835660945051093895, 2159449483938656978093695014156930904695073276185544390260923894390056236682698754475769727345306732241283513516715451298
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[ 89]]

A010161 Continued fraction for sqrt(89).

Original entry on oeis.org

9, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2, 18, 2, 3, 3, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			9.433981132056603811320660377... = 9 + 1/(2 + 1/(3 + 1/(3 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 10 2009

Links

Crossrefs

Cf. A010540 Decimal expansion. - Harry J. Smith, Jun 10 2009

Programs

  • Mathematica
    ContinuedFraction[Sqrt[89],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
LinearRecurrence[{0,0,0,0,1},{9,2,3,3,2,18},120] (* or *) PadRight[{9},120,{18,2,3,3,2}] (* Harvey P. Dale, Jan 20 2025 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(89)); for (n=0, 20000, write("b010161.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 10 2009

A041158 Numerators of continued fraction convergents to sqrt(89).

Original entry on oeis.org

9, 19, 66, 217, 500, 9217, 18934, 66019, 216991, 500001, 9217009, 18934019, 66019066, 216991217, 500001500, 9217018217, 18934037934, 66019132019, 216991433991, 500002000001, 9217027434009, 18934056868019, 66019198038066, 216991650982217, 500002500002500
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010540, A041159.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[89],30]] (* Harvey P. Dale, Jul 29 2012 *)

Formula

G.f.: -(x^9-9*x^8+19*x^7-66*x^6+217*x^5+500*x^4+217*x^3+66*x^2+19*x+9) / (x^10+1000*x^5-1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041159 Denominators of continued fraction convergents to sqrt(89).

Original entry on oeis.org

1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000, 977001, 2007002, 6998007, 23001023, 53000053, 977001977, 2007004007, 6998013998, 23001046001, 53000106000, 977002954001, 2007006014002, 6998020996007, 23001069002023, 53000159000053, 977003931002977
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041158, A010161, A020846, A010540.

Programs

  • Magma
    I:=[1, 2, 7, 23, 53, 977, 2007, 6998, 23001, 53000]; [n le 10 select I[n] else 1000*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
  • Mathematica
    Denominator/@Convergents[Sqrt[89], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^8 - 2 x^7 + 7 x^6 - 23 x^5 + 53 x^4 + 23 x^3 + 7 x^2 + 2 x + 1)/(x^10 + 1000 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0,0,0,0,1000,0,0,0,0,1},{1,2,7,23,53,977,2007,6998,23001,53000},30] (* Harvey P. Dale, Feb 07 2019 *)

Formula

G.f.: -(x^8-2*x^7+7*x^6-23*x^5+53*x^4+23*x^3+7*x^2+2*x+1) / (x^10+1000*x^5-1). - Colin Barker, Nov 14 2013
a(n) = 1000*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 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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