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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
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
C. Elsner, M. Stein, On Error Sum Functions Formed by Convergents of Real Numbers, J. Int. Seq. 14 (2011) # 11.8.6
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
Sequence in context: A353871 A275303 A281500 * A042367 A100341 A041869
KEYWORD
nonn,cofr,frac,easy
STATUS
approved