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.

A248319 Egyptian fraction representation of sqrt(96) (A010547) using a greedy function.

Original entry on oeis.org

9, 2, 4, 21, 2942, 53513091, 167326045060176459, 28151219628621255951104435939025563, 1114022548504683064752039841443977072775869961232641319345703597106467
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[ 96]]

A010167 Continued fraction for sqrt(96).

Original entry on oeis.org

9, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18, 1, 3, 1, 18
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			9.79795897113271239278913629... = 9 + 1/(1 + 1/(3 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 11 2009

Links

Crossrefs

Cf. A010547 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[96],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9},120,{18,1,3,1}] (* Harvey P. Dale, Apr 14 2020 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(96)); for (n=0, 20000, write("b010167.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

Formula

From Amiram Eldar, Nov 14 2023: (Start)
Multiplicative with a(2) = 3, 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) + 15/4^s). (End)

A041172 Numerators of continued fraction convergents to sqrt(96).

Original entry on oeis.org

9, 10, 39, 49, 921, 970, 3831, 4801, 90249, 95050, 375399, 470449, 8843481, 9313930, 36785271, 46099201, 866570889, 912670090, 3604581159, 4517251249, 84915103641, 89432354890, 353212168311
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010547, A041173.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[96],30]] (* Harvey P. Dale, Jan 31 2013 *)

Formula

G.f.: (9 + 10*x + 39*x^2 + 49*x^3 + 39*x^4 - 10*x^5 + 9*x^6 - x^7) / ((1 - 10*x^2 + x^4 )*(1 + 10*x^2 + x^4)). [Bruno Berselli, Oct 30 2013]

A177705 Decimal expansion of (3+2*sqrt(6))/5.

Original entry on oeis.org

1, 5, 7, 9, 7, 9, 5, 8, 9, 7, 1, 1, 3, 2, 7, 1, 2, 3, 9, 2, 7, 8, 9, 1, 3, 6, 2, 9, 8, 8, 2, 3, 5, 6, 5, 5, 6, 7, 8, 6, 3, 7, 8, 9, 9, 2, 2, 6, 2, 6, 6, 8, 0, 5, 1, 3, 7, 3, 0, 7, 7, 0, 2, 6, 9, 0, 0, 3, 8, 4, 1, 5, 0, 9, 8, 2, 9, 2, 6, 0, 1, 0, 6, 1, 5, 9, 4, 3, 7, 7, 3, 2, 4, 1, 8, 5, 6, 0, 9, 3, 9, 2, 7, 4, 3
Offset: 1

Views

Author

Klaus Brockhaus, May 11 2010

Keywords

Comments

Continued fraction expansion of (3+2*sqrt(6))/5 is A177704.

Examples

			(3+2*sqrt(6))/5 = 1.57979589711327123927...

Crossrefs

Cf. A010464, A010547, A177704.

Programs

  • Mathematica
    RealDigits[(3+2Sqrt[6])/5,10,150][[1]]  (* Harvey P. Dale, Mar 14 2011 *)

Formula

Equals (6+A010547)/10. - R. J. Mathar, Feb 03 2025
Showing 1-4 of 4 results.

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

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