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.

A248284 Egyptian fraction representation of sqrt(59) (A010512) using a greedy function.

Original entry on oeis.org

7, 2, 6, 70, 5172, 55202902, 8951438750970150, 99495402337297602079238688437886, 15492800774386064339112007474585245303291252482336052648764111003, 391698881553953026777765090845306600440609784819171044804973696937372852634612474031212566575806121439678866692229277539673721524
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[ 59]]

A010144 Continued fraction for sqrt(59).

Original entry on oeis.org

7, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2, 7, 2, 1, 14, 1, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			7.681145747868608175769687021... = 7 + 1/(1 + 1/(2 + 1/(7 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 07 2009

Links

Crossrefs

Cf. A010512 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[59],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
PadRight[{7},120,{14,1,2,7,2,1}] (* Harvey P. Dale, May 15 2017 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(59)); for (n=0, 20000, write("b010144.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

Formula

From Amiram Eldar, Nov 13 2023: (Start)
Multiplicative with a(2^e) = 2, a(3^e) = 7, and a(p^e) = 1 for p >= 5.
Dirichlet g.f.: zeta(s) * (1 + 1/2^s) * (1 + 2/3^(s-1)). (End)

A041102 Numerators of continued fraction convergents to sqrt(59).

Original entry on oeis.org

7, 8, 23, 169, 361, 530, 7781, 8311, 24403, 179132, 382667, 561799, 8247853, 8809652, 25867157, 189879751, 405626659, 595506410, 8742716399, 9338222809, 27419162017, 201272356928, 429963875873
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010512, A041103.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[59],40]] (* or *) LinearRecurrence[ {0,0,0,0,0,1060,0,0,0,0,0,-1},{7,8,23,169,361,530,7781,8311,24403,179132,382667,561799},40] (* Harvey P. Dale, Nov 25 2012 *)
CoefficientList[Series[- (x^11 - 7 x^10 + 8 x^9 - 23 x^8 + 169 x^7 - 361 x^6 - 530 x^5 - 361 x^4 - 169 x^3 - 23 x^2 - 8 x - 7)/(x^12 - 1060 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 25 2013 *)

Formula

a(n) = 1060*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+8*x^9-23*x^8+169*x^7-361*x^6-530*x^5-361*x^4-169*x^3-23*x^2-8*x-7)/(x^12-1060*x^6+1). [Colin Barker, Jul 18 2012]

A041103 Denominators of continued fraction convergents to sqrt(59).

Original entry on oeis.org

1, 1, 3, 22, 47, 69, 1013, 1082, 3177, 23321, 49819, 73140, 1073779, 1146919, 3367617, 24720238, 52808093, 77528331, 1138204727, 1215733058, 3569670843, 26203428959, 55976528761, 82179957720
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010512, A041102.

Programs

  • Mathematica
    Denominator[Convergents[Sqrt[59], 30]] (* Vincenzo Librandi, Oct 24 2013 *)

Formula

a(n) = 1060*a(n-6)-a(n-12). G.f.: -(x^10-x^9+3*x^8-22*x^7+47*x^6-69*x^5-47*x^4-22*x^3-3*x^2-x-1)/(x^12-1060*x^6+1). [Colin Barker, Jul 18 2012]
Showing 1-4 of 4 results.

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

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