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A041018 Numerators of continued fraction convergents to sqrt(13). 11
3, 4, 7, 11, 18, 119, 137, 256, 393, 649, 4287, 4936, 9223, 14159, 23382, 154451, 177833, 332284, 510117, 842401, 5564523, 6406924, 11971447, 18378371, 30349818, 200477279, 230827097, 431304376, 662131473 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Johannes W. Meijer, Jun 12 2010: (Start)

The a(n) terms of this sequence can be constructed with the terms of sequence A006497.

For the terms of the periodical sequence of the continued fraction for sqrt(13) see A010122. We observe that its period is five. The decimal expansion of sqrt(13) is A010470. (End)

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,36,0,0,0,0,1).

FORMULA

From Johannes W. Meijer, Jun 12 2010: (Start)

a(5*n) = A006497(3*n+1), a(5*n+1) = (A006497(3*n+2)-A006497(3*n+1))/2, a(5*n+2) = (A006497(3*n+2)+A006497(3*n+1))/2, a(5*n+3) = A006497(3*n+2) and a(5*n+4) = A006497(3*n+3)/2.

(End)

G.f.: (3 + 4*x + 7*x^2 + 11*x^3 + 18*x^4 + 11*x^5 - 7*x^6 + 4*x^7 - 3*x^8 + x^9)/(1 - 36*x^5 - x^10) - Peter J. C. Moses, Jul 29 2013

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[13], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)

Numerator[Convergents[Sqrt[13], 30]] (* Vincenzo Librandi, Oct 27 2013 *)

CROSSREFS

Cf. A010470, A041019 (denominators), A041046, A041090, A041150, A041226, A041318, A041426 and A041550.

Sequence in context: A293420 A041739 A042593 * A072255 A049863 A025068

Adjacent sequences:  A041015 A041016 A041017 * A041019 A041020 A041021

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 18 15:33 EST 2018. Contains 299324 sequences. (Running on oeis4.)