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A041079 Denominators of continued fraction convergents to sqrt(46). 2
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 (list; graph; refs; listen; history; text; internal format)
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A. J. van der Poorten, An introduction to continued fractions, Unpublished.

A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]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

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Last modified September 23 15:23 EDT 2021. Contains 347618 sequences. (Running on oeis4.)