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.

A248255 Egyptian fraction representation of sqrt(28) (A010483) using a greedy function.

Original entry on oeis.org

5, 4, 25, 666, 892358, 830113252100, 6890868531517036908804204, 765564099160305273559925342798919694764879717405690, 681027718799553552099401892363533829797246440808729714034620705787624761700369516608168143683921127348
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[ 28]]

A040022 Continued fraction for sqrt(28).

Original entry on oeis.org

5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			5.29150262212918118100323150... = 5 + 1/(3 + 1/(2 + 1/(3 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009

References

  • James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Links

Crossrefs

Cf. A010483 Decimal expansion. - Harry J. Smith, Jun 04 2009

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[28], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{5},120,{10,3,2,3}] (* Harvey P. Dale, Aug 13 2024 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(28)); for (n=0, 20000, write("b040022.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Formula

G.f.: (5 + 3*x + 2*x^2 + 3*x^3 + 5*x^4)/(1 - x^4). - Stefano Spezia, Jul 26 2025

A041044 Numerators of continued fraction convergents to sqrt(28).

Original entry on oeis.org

5, 16, 37, 127, 1307, 4048, 9403, 32257, 331973, 1028176, 2388325, 8193151, 84319835, 261152656, 606625147, 2081028097, 21416906117, 66331746448, 154080399013, 528572943487, 5439809833883, 16848002445136
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010483, A041045.

Programs

  • Mathematica
    Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[28],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
CoefficientList[Series[- (x^7 - 5 x^6 + 16 x^5 - 37 x^4 - 127 x^3 - 37 x^2 - 16 x - 5)/((x^4 - 16 x^2 + 1) (x^4 + 16 x^2 + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)

Formula

a(n) = 254*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+16*x^5-37*x^4-127*x^3-37*x^2-16*x-5)/((x^4-16*x^2+1)*(x^4+16*x^2+1)). [Colin Barker, Jul 16 2012]

A171540 Decimal expansion of sqrt(5/14).

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Dec 11 2009

Keywords

Comments

The absolute value of the Clebsch-Gordan coupling coefficient = <2 3/2 ; -1 1/2 | 5/2 -1/2>.

Examples

			sqrt(5/14) = sqrt(70)/14 = 0.597614304667196819984408589846...

Links

Programs

  • Mathematica
    RealDigits[Sqrt[5/14],10,120][[1]] (* Harvey P. Dale, Oct 19 2012 *)

Formula

equals A002163/A010471 = A010467/A010483.
Showing 1-4 of 4 results.

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

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