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 1-3 of 3 results.

A010475 Decimal expansion of square root of 19.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

Continued fraction expansion is 4 followed by {2, 1, 3, 1, 2, 8} repeated. - Harry J. Smith, Jun 03 2009

Examples

			4.358898943540673552236981983859615659137003925232444936890344138159557....

Links

Crossrefs

Cf. A010124 (continued fraction).

Programs

  • Mathematica
    RealDigits[N[Sqrt[19],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)
  • PARI
    default(realprecision, 20080); x=sqrt(19); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010475.txt", n, " ", d));  \\ Harry J. Smith, Jun 03 2009

A041028 Numerators of continued fraction convergents to sqrt(19).

Original entry on oeis.org

4, 9, 13, 48, 61, 170, 1421, 3012, 4433, 16311, 20744, 57799, 483136, 1024071, 1507207, 5545692, 7052899, 19651490, 164264819, 348181128, 512445947, 1885518969, 2397964916, 6681448801, 55849555324
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010124, A010475, A041029.

Programs

  • Mathematica
    Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[19],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
CoefficientList[Series[- (x^11 - 4 x^10 + 9 x^9 - 13 x^8 + 48 x^7 - 61 x^6 - 170 x^5 - 61 x^4 - 48 x^3 - 13 x^2 - 9 x - 4)/(x^12 - 340 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{0,0,0,0,0,340,0,0,0,0,0,-1},{4,9,13,48,61,170,1421,3012,4433,16311,20744,57799},30] (* or *) Numerator[ Convergents[ Sqrt[19],30]] (* Harvey P. Dale, Jul 04 2021 *)

Formula

a(n) = 340*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +9*x^9 -13*x^8 +48*x^7 -61*x^6 -170*x^5 -61*x^4 -48*x^3 -13*x^2 -9*x -4)/(x^12-340*x^6+1). [Colin Barker, Jul 16 2012]

A041029 Denominators of continued fraction convergents to sqrt(19).

Original entry on oeis.org

1, 2, 3, 11, 14, 39, 326, 691, 1017, 3742, 4759, 13260, 110839, 234938, 345777, 1272269, 1618046, 4508361, 37684934, 79878229, 117563163, 432567718, 550130881, 1532829480, 12812766721, 27158362922
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010124, A010475, A041028.

Programs

  • Mathematica
    Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[19],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 11 x^7 + 14 x^6 - 39 x^5 - 14 x^4 - 11 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 340 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)

Formula

a(n) = 340*a(n-6)-a(n-12). G.f.: -(x^10- 2*x^9+ 3*x^8 -11*x^7 +14*x^6 -39*x^5 -14*x^4 -11*x^3 -3*x^2 -2*x -1)/(x^12-340*x^6+1). [Colin Barker, Jul 16 2012]
Showing 1-3 of 3 results.

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

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