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.

A248277 Egyptian fraction representation of sqrt(52) (A010505) using a greedy function.

Original entry on oeis.org

7, 5, 91, 8808, 147334267, 630308457230044767, 705412662885103424818861300802350580, 5393679030808484908733796582654864706316301359628528840178094089020230098
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[ 52]]

A010138 Continued fraction for sqrt(52).

Original entry on oeis.org

7, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1, 2, 1, 4, 14, 4, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			7.211102550927978586238442534... = 7 + 1/(4 + 1/(1 + 1/(2 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 06 2009

Links

Crossrefs

Cf. A010505 Decimal expansion. - Harry J. Smith, Jun 06 2009

Programs

  • Mathematica
    ContinuedFraction[Sqrt[52],300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)
PadRight[{7},120,{14,4,1,2,1,4}] (* Harvey P. Dale, Nov 22 2018 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(52)); for (n=0, 20000, write("b010138.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 06 2009

A041088 Numerators of continued fraction convergents to sqrt(52).

Original entry on oeis.org

7, 29, 36, 101, 137, 649, 9223, 37541, 46764, 131069, 177833, 842401, 11971447, 48728189, 60699636, 170127461, 230827097, 1093435849, 15538928983, 63249151781, 78788080764, 220825313309, 299613394073
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010505, A041089.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[52], 30]] (* Vincenzo Librandi, Oct 25 2013 *)

Formula

a(n) = 1298*a(n-6)-a(n-12). G.f.: -(x^11-7*x^10+29*x^9-36*x^8+101*x^7-137*x^6-649*x^5-137*x^4-101*x^3-36*x^2-29*x-7)/((x^2-3*x-1)*(x^2+3*x-1)*(x^4-3*x^3+10*x^2+3*x+1)*(x^4+3*x^3+10*x^2-3*x+1)). [Colin Barker, Jul 18 2012]

A041089 Denominators of continued fraction convergents to sqrt(52).

Original entry on oeis.org

1, 4, 5, 14, 19, 90, 1279, 5206, 6485, 18176, 24661, 116820, 1660141, 6757384, 8417525, 23592434, 32009959, 151632270, 2154861739, 8771079226, 10925940965, 30622961156, 41548902121, 196818569640, 2797008877081, 11384854077964, 14181862955045, 39748579988054
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010505, A041088.

Programs

Formula

a(n) = 1298*a(n-6)-a(n-12). G.f.: -(x^10-4*x^9+5*x^8-14*x^7+19*x^6-90*x^5-19*x^4-14*x^3-5*x^2-4*x-1)/((x^2-3*x-1)*(x^2+3*x-1)*(x^4-3*x^3+10*x^2+3*x+1)*(x^4+3*x^3+10*x^2-3*x+1)). [Colin Barker, Jul 18 2012]
Showing 1-4 of 4 results.

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

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