A041009 Denominators of continued fraction convergents to sqrt(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

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: A353871 A275303 A281500 * A042367 A100341 A041869

Adjacent sequences: A041006 A041007 A041008 * A041010 A041011 A041012

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved