A041079 Denominators of continued fraction convergents to sqrt(46).

1, 1, 4, 5, 9, 23, 147, 317, 464, 781, 2807, 3588, 45863, 49451, 194216, 243667, 437883, 1119433, 7154481, 15428395, 22582876, 38011271, 136616689, 174627960, 2232152209, 2406780169, 9452492716, 11859272885

Offset

0,3

Comments

46 is the smallest value of n for which the period of the continued fraction convergents to sqrt(n) is 12. [Colin Barker, Jul 19 2012]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

A. J. van der Poorten, An introduction to continued fractions, Unpublished.

A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,48670,0,0,0,0,0,0,0,0,0,0,0,-1).

Formula

a(n) = 48670*a(n-12)-a(n-24). G.f.: -(x^22 -x^21 +4*x^20 -5*x^19 +9*x^18 -23*x^17 +147*x^16 -317*x^15 +464*x^14 -781*x^13 +2807*x^12 -3588*x^11 -2807*x^10 -781*x^9 -464*x^8 -317*x^7 -147*x^6 -23*x^5 -9*x^4 -5*x^3 -4*x^2 -x -1) / (x^24-48670*x^12+1). [Colin Barker, Jul 19 2012]

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[46], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011*)
Denominator[Convergents[Sqrt[46], 30]] (* Vincenzo Librandi, Oct 24 2013 *)

Crossrefs

Cf. A010500, A041078.

Sequence in context: A041993 A153068 A075116 * A042715 A163868 A019148

Adjacent sequences: A041076 A041077 A041078 * A041080 A041081 A041082

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

Formula corrected by Colin Barker, Jul 24 2012

Status

approved