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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010465, A041008.

Programs

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 *)

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