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.

A177935 Decimal expansion of sqrt(107).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, May 15 2010

Keywords

Comments

Continued fraction expansion of sqrt(107) is A010173.

Examples

			sqrt(107) = 10.34408043278860046973...

Crossrefs

Cf. A177934 (decimal expansion of sqrt(71216963807)), A010173 (10 followed by (repeat 2, 1, 9, 1, 2, 20)).

Programs

  • Mathematica
    RealDigits[Sqrt[107],10,120][[1]] (* Harvey P. Dale, Apr 25 2014 *)

A041192 Numerators of continued fraction convergents to sqrt(107).

Original entry on oeis.org

10, 21, 31, 300, 331, 962, 19571, 40104, 59675, 577179, 636854, 1850887, 37654594, 77160075, 114814669, 1110492096, 1225306765, 3561105626, 72447419285, 148455944196, 220903363481, 2136586215525, 2357489579006
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041193 (denominators), A010173 (continued fraction), A177935 (decimal expansion).

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[107], 30]] (* Vincenzo Librandi, Oct 26 2013 *)

Formula

a(n) = 1924*a(n-6)-a(n-12). G.f.: -(x^11-10*x^10+21*x^9-31*x^8+300*x^7-331*x^6-962*x^5-331*x^4-300*x^3-31*x^2-21*x-10)/(x^12-1924*x^6+1). [Colin Barker, Jul 19 2012]

A041193 Denominators of continued fraction convergents to sqrt(107).

Original entry on oeis.org

1, 2, 3, 29, 32, 93, 1892, 3877, 5769, 55798, 61567, 178932, 3640207, 7459346, 11099553, 107355323, 118454876, 344265075, 7003756376, 14351777827, 21355534203, 206551585654, 227907119857, 662365825368
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041192 (numerators), A010173 (continued fraction), A177935 (decimal expansion).

Programs

  • Mathematica
    Denominator[Convergents[Sqrt[107],30]] (* or *) LinearRecurrence[ {0,0,0,0,0,1924,0,0,0,0,0,-1},{1,2,3,29,32,93,1892,3877,5769,55798,61567,178932},30] (* Harvey P. Dale, Aug 30 2013 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 29 x^7 + 32 x^6 - 93 x^5 - 32 x^4 - 29 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 1924 x^6 + 1), {x, 0, 30}], x]  (* Vincenzo Librandi, Oct 24 2013 *)

Formula

a(n) = 1924*a(n-6)-a(n-12). G.f.: -(x^10-2*x^9+3*x^8-29*x^7+32*x^6 -93*x^5 -32*x^4-29*x^3-3*x^2-2*x-1) / (x^12-1924*x^6+1). - Colin Barker, Jul 19 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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