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.

A248292 Egyptian fraction representation of sqrt(68) (A010520) using a greedy function.

Original entry on oeis.org

8, 5, 22, 1322, 3621500, 17445297363138, 776156771532279826926457191, 1125673063406602593902433484734481317497130098734266573, 2359563766366828684685276326098059577152401128042629265861141526556488039378108148960279616218064655420661149
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[ 68]]

A040059 Continued fraction for sqrt(68).

Original entry on oeis.org

8, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			8.2462112512353210996428197... = 8 + 1/(4 + 1/(16 + 1/(4 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 08 2009

Links

Crossrefs

Cf. A010520 Decimal expansion. - Harry J. Smith, Jun 08 2009

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[68],300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 37000); x=contfrac(sqrt(68)); for (n=0, 20000, write("b040059.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 08 2009

A041118 Numerators of continued fraction convergents to sqrt(68).

Original entry on oeis.org

8, 33, 536, 2177, 35368, 143649, 2333752, 9478657, 153992264, 625447713, 10161155672, 41270070401, 670482282088, 2723199198753, 44241669462136, 179689877047297, 2919279702218888, 11856808685922849, 192628218676984472, 782369683393860737, 12710543152978756264
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010520, A041119.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[68],30]] (* Harvey P. Dale, Aug 12 2012 *)

Formula

G.f.: -(x^3-8*x^2-33*x-8) / ((x^2-8*x-1)*(x^2+8*x-1)). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041119 Denominators of continued fraction convergents to sqrt(68).

Original entry on oeis.org

1, 4, 65, 264, 4289, 17420, 283009, 1149456, 18674305, 75846676, 1232221121, 5004731160, 81307919681, 330236409884, 5365090477825, 21790598321184, 354014663616769, 1437849252788260, 23359602708228929, 94876260085703976, 1541379764079492545
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041118, A040059, A020825, A010520.

Programs

  • Magma
    I:=[1, 4, 65, 264]; [n le 4 select I[n] else 66*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[68],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
Denominator[Convergents[Sqrt[68], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

Formula

G.f.: -(x^2-4*x-1) / ((x^2-8*x-1)*(x^2+8*x-1)). - Colin Barker, Nov 13 2013
a(n) = 66*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 13 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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