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.

A248298 Egyptian fraction representation of sqrt(74) (A010526) using a greedy function.

Original entry on oeis.org

8, 2, 10, 431, 196796, 42222589233, 4119127882822681368069, 22394712126990929163352329336575823966927304, 810283246500627303789590552867279442902569752132975902553147296681478084954900646327035
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[ 74]]

A010152 Continued fraction for sqrt(74).

Original entry on oeis.org

8, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			8.602325267042626771729473535... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 09 2009

Links

Crossrefs

Cf. A010526 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[74],300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
PadRight[{8},120,{16,1,1,1,1}] (* Harvey P. Dale, Nov 14 2013 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(74)); for (n=0, 20000, write("b010152.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 09 2009

Formula

From Amiram Eldar, Nov 13 2023: (Start)
Multiplicative with a(5^e) = 16, and a(p^e) = 1 for p != 5.
Dirichlet g.f.: zeta(s) * (1 + 3/5^(s-1)). (End)

A041130 Numerators of continued fraction convergents to sqrt(74).

Original entry on oeis.org

8, 9, 17, 26, 43, 714, 757, 1471, 2228, 3699, 61412, 65111, 126523, 191634, 318157, 5282146, 5600303, 10882449, 16482752, 27365201, 454325968, 481691169, 936017137, 1417708306, 2353725443, 39077315394, 41431040837, 80508356231, 121939397068, 202447753299
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010526, A041131.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[74], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
LinearRecurrence[{0,0,0,0,86,0,0,0,0,1},{8,9,17,26,43,714,757,1471,2228,3699},40] (* Harvey P. Dale, Sep 18 2024 *)

Formula

G.f.: -(x^9-8*x^8+9*x^7-17*x^6+26*x^5+43*x^4+26*x^3+17*x^2+9*x+8) / (x^10+86*x^5-1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013

A041131 Denominators of continued fraction convergents to sqrt(74).

Original entry on oeis.org

1, 1, 2, 3, 5, 83, 88, 171, 259, 430, 7139, 7569, 14708, 22277, 36985, 614037, 651022, 1265059, 1916081, 3181140, 52814321, 55995461, 108809782, 164805243, 273615025, 4542645643, 4816260668, 9358906311, 14175166979, 23534073290, 390720339619, 414254412909
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041130, A010152, A020831, A010526.

Programs

  • Magma
    I:=[1, 1, 2, 3, 5, 83, 88, 171, 259, 430]; [n le 10 select I[n] else 86*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator/@Convergents[Sqrt[74], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
CoefficientList[Series[-(x^4 - 3 x^3 + 4 x^2 - 2 x + 1) (x^4 + 2 x^3 + 4 x^2 + 3 x + 1)/(x^10 + 86 x^5 - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,0,86,0,0,0,0,1},{1,1,2,3,5,83,88,171,259,430},50] (* Harvey P. Dale, Nov 09 2017 *)

Formula

G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+86*x^5-1). - Colin Barker, Nov 13 2013
a(n) = 86*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 11 2013
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.