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.

A248276 Egyptian fraction representation of sqrt(51) (A010504) using a greedy function.

Original entry on oeis.org

7, 8, 61, 28583, 11215712908, 163912730694765446902, 323312653298355913241854107936424272297052, 282221573696620922018917798450701835109135899750274145244297035015729916105092332416
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[ 51]]

A040043 Continued fraction for sqrt(51).

Original entry on oeis.org

7, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7, 14, 7
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			7.1414284285428499979993998... = 7 + 1/(7 + 1/(14 + 1/(7 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 06 2009

Links

Crossrefs

Cf. A010504 Decimal expansion. - Harry J. Smith, Jun 06 2009

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[51],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
PadRight[{7},120,{14,7}] (* Harvey P. Dale, May 22 2020 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 41000); x=contfrac(sqrt(51)); for (n=0, 20000, write("b040043.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

A041086 Numerators of continued fraction convergents to sqrt(51).

Original entry on oeis.org

7, 50, 707, 4999, 70693, 499850, 7068593, 49980001, 706788607, 4997500250, 70671792107, 499700044999, 7066472422093, 49965006999650, 706576570417193, 4996000999920001, 70650590569297207, 499550134985000450, 7064352480359303507, 49950017497500124999
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041087, A010504.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[51], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,100,0,-1},{7,50,707,4999},20] (* Harvey P. Dale, Dec 04 2014 *)

Formula

G.f.: -(x^3-7*x^2-50*x-7) / (x^4-100*x^2+1). - Colin Barker, Nov 04 2013

Extensions

More terms from Colin Barker, Nov 04 2013

A087477 Decimal expansion of sqrt(51)-4.

Original entry on oeis.org

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

Views

Author

Zak Seidov, Sep 09 2003

Keywords

Comments

A simple approximation to Pi, see also A087478.

Examples

			3.14142842854284999799939981136726527876617115990273...

Links

Crossrefs

Cf. A000796, A010504, A087478.

Programs

  • Mathematica
    RealDigits[Sqrt[51] - 4, 10, 120][[1]] (* Amiram Eldar, May 16 2023 *)

Formula

Equals A010504 minus 4. - R. J. Mathar, Sep 11 2008
Showing 1-4 of 4 results.

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

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