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.

A248282 Egyptian fraction representation of sqrt(57) (A010510) using a greedy function.

Original entry on oeis.org

7, 2, 21, 452, 333526, 239840839427, 213854001335207704440895, 285250080311453944844806600568111651628374758476, 116331150526334053652977740551831381838315865368775202070425604169497427887617729415451917178949
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[ 57]]

A010142 Continued fraction for sqrt(57).

Original entry on oeis.org

7, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1, 4, 1, 1, 14, 1, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			7.549834435270749697236684806... = 7 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 06 2009

Links

Crossrefs

Cf. A010510 Decimal expansion. - Harry J. Smith, Jun 06 2009

Programs

  • Mathematica
    ContinuedFraction[Sqrt[57],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
PadRight[{7},120,{14,1,1,4,1,1}] (* Harvey P. Dale, Mar 28 2016 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(57)); for (n=0, 20000, write("b010142.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

A041098 Numerators of continued fraction convergents to sqrt(57).

Original entry on oeis.org

7, 8, 15, 68, 83, 151, 2197, 2348, 4545, 20528, 25073, 45601, 663487, 709088, 1372575, 6199388, 7571963, 13771351, 200370877, 214142228, 414513105, 1872194648, 2286707753, 4158902401, 60511341367
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010510, A041099.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[57], 30]] (* Vincenzo Librandi, Oct 25 2013 *)
LinearRecurrence[{0,0,0,0,0,302,0,0,0,0,0,-1},{7,8,15,68,83,151,2197,2348,4545,20528,25073,45601},30] (* Harvey P. Dale, Jul 22 2016 *)

Formula

a(n) = 302*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+8*x^9-15*x^8+68*x^7-83*x^6-151*x^5-83*x^4-68*x^3-15*x^2-8*x-7)/(x^12-302*x^6+1). [Colin Barker, Jul 18 2012]

A041099 Denominators of continued fraction convergents to sqrt(57).

Original entry on oeis.org

1, 1, 2, 9, 11, 20, 291, 311, 602, 2719, 3321, 6040, 87881, 93921, 181802, 821129, 1002931, 1824060, 26539771, 28363831, 54903602, 247978239, 302881841, 550860080, 8014922961, 8565783041, 16580706002
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010510, A041098.

Programs

  • Mathematica
    Denominator[Convergents[Sqrt[57], 30]] (* Vincenzo Librandi, Oct 24 2013 *)

Formula

From Colin Barker, Jul 18 2012: (Start)
a(n) = 302*a(n-6)-a(n-12).
G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-10*x^3-1)/(x^12-302*x^6+1). (End)
Showing 1-4 of 4 results.

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

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