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A041008 Numerators of continued fraction convergents to sqrt(7). 6
2, 3, 5, 8, 37, 45, 82, 127, 590, 717, 1307, 2024, 9403, 11427, 20830, 32257, 149858, 182115, 331973, 514088, 2388325, 2902413, 5290738, 8193151, 38063342, 46256493, 84319835, 130576328, 606625147 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

C. Elsner, Series of Error Terms for Rational Approximations of Irrational Numbers , J. Int. Seq. 14 (2011) # 11.1.4

C. Elsner, M. Stein, On Error Sum Functions Formed by Convergents of Real Numbers, J. Int. Seq. 14 (2011) # 11.8.6

Index entries for linear recurrences with constant coefficients, signature (0,0,0,16,0,0,0,-1).

FORMULA

G.f.: (2+3*x+5*x^2+8*x^3+5*x^4-3*x^5+2*x^6-x^7)/(1-16*x^4+x^8)

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[7], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*)

Numerator[Convergents[Sqrt[7], 30]] (* Vincenzo Librandi, Oct 28 2013 *)

CROSSREFS

Cf. A010465, A041009, A266698 (quadrisection), A001081 (quadrisection)

Sequence in context: A281618 A059359 A042069 * A041569 A268480 A128485

Adjacent sequences:  A041005 A041006 A041007 * A041009 A041010 A041011

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 22 20:41 EDT 2019. Contains 326195 sequences. (Running on oeis4.)