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.

A248315 Egyptian fraction representation of sqrt(92) (A010543) using a greedy function.

Original entry on oeis.org

9, 2, 11, 1327, 2658064, 22045059363790, 559876050162626752359764113, 970079383648139591179184216503267475762543140383282948, 1139782885752855378769274684680386640437890911588437912190474154597375065048854063128961470289155028588836525
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.
Cf. A010543.

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[ 92]]

A010163 Continued fraction for sqrt(92).

Original entry on oeis.org

9, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2, 1, 1, 18, 1, 1, 2, 4, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			9.591663046625439083194876128... = 9 + 1/(1 + 1/(1 + 1/(2 + 1/(4 + ...)))) \\ _Harry J. Smith_, Jun 11 2009

Links

Crossrefs

Cf. A010543 Decimal expansion. - Harry J. Smith, Jun 11 2009

Programs

  • Mathematica
    ContinuedFraction[Sqrt[92],300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(92)); for (n=0, 20000, write("b010163.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 11 2009

A041164 Numerators of continued fraction convergents to sqrt(92).

Original entry on oeis.org

9, 10, 19, 48, 211, 470, 681, 1151, 21399, 22550, 43949, 110448, 485741, 1081930, 1567671, 2649601, 49260489, 51910090, 101170579, 254251248, 1118175571, 2490602390, 3608777961, 6099380351, 113397624279, 119497004630, 232894628909, 585286262448
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010543, A041165.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[92], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

G.f.: -(x^15 -9*x^14 +10*x^13 -19*x^12 +48*x^11 -211*x^10 +470*x^9 -681*x^8 -1151*x^7 -681*x^6 -470*x^5 -211*x^4 -48*x^3 -19*x^2 -10*x -9) / ((x^8 -48*x^4 +1)*(x^8 +48*x^4 +1)). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041165 Denominators of continued fraction convergents to sqrt(92).

Original entry on oeis.org

1, 1, 2, 5, 22, 49, 71, 120, 2231, 2351, 4582, 11515, 50642, 112799, 163441, 276240, 5135761, 5412001, 10547762, 26507525, 116577862, 259663249, 376241111, 635904360, 11822519591, 12458423951, 24280943542, 61020311035, 268362187682, 597744686399
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041164, A010163, A020849, A010543.

Programs

  • Magma
    I:=[1, 1, 2, 5, 22, 49, 71, 120, 2231, 2351, 4582, 11515, 50642, 112799, 163441, 276240]; [n le 16 select I[n] else 2302*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
  • Mathematica
    Denominator[Convergents[Sqrt[92], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

Formula

G.f.: -(x^14 -x^13 +2*x^12 -5*x^11 +22*x^10 -49*x^9 +71*x^8 -120*x^7 -71*x^6 -49*x^5 -22*x^4 -5*x^3 -2*x^2 -x -1) / ((x^8 -48*x^4 +1)*(x^8 +48*x^4 +1)). - Colin Barker, Nov 14 2013
a(n) = 2302*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

Extensions

More terms from Colin Barker, Nov 14 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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