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 1-5 of 5 results.

A248301 Egyptian fraction representation of sqrt(77) (A010529) using a greedy function.

Original entry on oeis.org

8, 2, 4, 41, 1742, 11028177, 162993884286434, 98590211385064017280363413293, 12117436325243830366668048782511200599594547426236327606671, 1005207586152279178371805242956335367687650840213497606799698333833564307176435895593356718339151523032260919541519453
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[ 77]]

A010155 Continued fraction for sqrt(77).

Original entry on oeis.org

8, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3, 2, 3, 1, 16, 1, 3
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			8.774964387392122060406388307... = 8 + 1/(1 + 1/(3 + 1/(2 + 1/(3 + ...)))). - _Harry J. Smith_, Jun 09 2009

Links

Crossrefs

Cf. A010529 Decimal expansion. - Harry J. Smith, Jun 09 2009

Programs

  • Mathematica
    ContinuedFraction[Sqrt[77],300] (* Vladimir Joseph Stephan Orlovsky, Mar 09 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 20000); x=contfrac(sqrt(77)); for (n=0, 20000, write("b010155.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

A041136 Numerators of continued fraction convergents to sqrt(77).

Original entry on oeis.org

8, 9, 35, 79, 272, 351, 5888, 6239, 24605, 55449, 190952, 246401, 4133368, 4379769, 17272675, 38925119, 134048032, 172973151, 2901618448, 3074591599, 12125393245, 27325378089, 94101527512
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010529, A041137.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[77], 30]] (* Vincenzo Librandi, Oct 26 2013 *)

Formula

a(n) = 702*a(n-6)-a(n-12). G.f.: -(x^11-8*x^10+9*x^9-35*x^8+79*x^7-272*x^6-351*x^5-272*x^4-79*x^3-35*x^2-9*x-8)/((x^4-9*x^2+1)*(x^8+9*x^6+80*x^4+9*x^2+1)). [Colin Barker, Jul 18 2012]

A041137 Denominators of continued fraction convergents to sqrt(77).

Original entry on oeis.org

1, 1, 4, 9, 31, 40, 671, 711, 2804, 6319, 21761, 28080, 471041, 499121, 1968404, 4435929, 15276191, 19712120, 330670111, 350382231, 1381816804, 3114015839, 10723864321, 13837880160, 232129946881, 245967827041, 970033428004, 2186034683049, 7528137477151
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010529, A041136.

Programs

  • Mathematica
    Denominator/@Convergents[Sqrt[77], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[- (x^10 - x^9 + 4 x^8 - 9 x^7 + 31 x^6 - 40 x^5 - 31 x^4 - 9 x^3 - 4 x^2 - x - 1)/((x^4 - 9 x^2 + 1) (x^8 + 9 x^6 + 80 x^4 + 9 x^2 + 1)), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 24 2013 *)

Formula

a(n) = 702*a(n-6)-a(n-12). G.f.: -(x^10-x^9+4*x^8-9*x^7+31*x^6-40*x^5-31*x^4-9*x^3-4*x^2-x-1)/((x^4-9*x^2+1)*(x^8+9*x^6+80*x^4+9*x^2+1)). [Colin Barker, Jul 18 2012]

A176017 Decimal expansion of (7+sqrt(77))/14.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 06 2010

Keywords

Comments

Continued fraction expansion of (7+sqrt(77))/14 is A010688.

Examples

			(7+sqrt(77))/14 = 1.12678317052800871860...

Crossrefs

Cf. A010529 (decimal expansion of sqrt(77)), A010688 (repeat 1, 7).

Programs

  • Mathematica
    RealDigits[(7+Sqrt[77])/14,10,120][[1]] (* Harvey P. Dale, Oct 15 2013 *)
Showing 1-5 of 5 results.

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

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