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 A041009 Denominators of continued fraction convergents to sqrt(7). 7
 1, 1, 2, 3, 14, 17, 31, 48, 223, 271, 494, 765, 3554, 4319, 7873, 12192, 56641, 68833, 125474, 194307, 902702, 1097009, 1999711, 3096720, 14386591, 17483311, 31869902, 49353213, 229282754, 278635967 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sqrt(7) = 2 + 9/14 + 9/(14*223) + 9/(223*3554) + 9/(3554*56641)...; sum of these 5 terms = 2.64575131088, with sqrt(7) = 2.64575131106... The terms 14, 223, 3554,...= a(4), a(8), a(12),... - Gary W. Adamson, Dec 27 2007 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 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.: (1+x+2*x^2+3*x^3-2*x^4+x^5-x^6)/(1-16*x^4+x^8). [Colin Barker, Mar 13 2012] MATHEMATICA Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[7], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 16 2011*) Denominator[Convergents[Sqrt[7], 30]] (* or *) LinearRecurrence[ {0, 0, 0, 16, 0, 0, 0, -1}, {1, 1, 2, 3, 14, 17, 31, 48}, 30] (* Harvey P. Dale, Dec 17 2019 *) CROSSREFS Cf. A010465, A041008. Sequence in context: A260143 A275303 A281500 * A042367 A100341 A041869 Adjacent sequences:  A041006 A041007 A041008 * A041010 A041011 A041012 KEYWORD nonn,cofr,frac,easy AUTHOR STATUS approved

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)