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.

A248318 Egyptian fraction representation of sqrt(95) (A010546) using a greedy function.

Original entry on oeis.org

9, 2, 5, 22, 747, 899873, 1220923268615, 10510990350737693696021245, 316206307289858390044039445912464508089748171542815, 567822847346091249962050158000755056694537727317382487188197252275025245246033509041171437550989931224
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[ 95]]

A010166 Continued fraction for sqrt(95).

Original entry on oeis.org

9, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18, 1, 2, 1, 18
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			9.74679434480896390683841319... = 9 + 1/(1 + 1/(2 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 11 2009

Links

Crossrefs

Cf. A010546 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[95],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 20000); x=contfrac(sqrt(95)); for (n=0, 20000, write("b010166.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

Formula

From Amiram Eldar, Nov 14 2023: (Start)
Multiplicative with a(2) = 2, a(2^e) = 18 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 1/2^s + 1/4^(s-2)). (End)

A041170 Numerators of continued fraction convergents to sqrt(95).

Original entry on oeis.org

9, 10, 29, 39, 731, 770, 2271, 3041, 57009, 60050, 177109, 237159, 4445971, 4683130, 13812231, 18495361, 346728729, 365224090, 1077176909, 1442400999, 27040394891, 28482795890, 84005986671
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010546, A041171.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[95], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,0,0,78,0,0,0,-1},{9,10,29,39,731,770,2271,3041},30] (* Harvey P. Dale, Dec 30 2020 *)

Formula

G.f.: (9 +10*x +29*x^2 +39*x^3 +29*x^4 -10*x^5 +9*x^6 -x^7) / (1 -78*x^4 +x^8). [Bruno Berselli, Oct 30 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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