OFFSET
0,1
COMMENTS
Eventual period is (3,6). - Zak Seidov, Mar 05 2011
REFERENCES
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง4.4 Powers and Roots, p. 144.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac.
Index entries for linear recurrences with constant coefficients, signature (0,1).
FORMULA
From Stefano Spezia, Jan 18 2025: (Start)
G.f.: 3*(1 + x + x^2)/(1 - x^2).
E.g.f.: 3*(2*cosh(x) + sinh(x) - 1). (End)
EXAMPLE
3.316624790355399849114932736... = 3 + 1/(3 + 1/(6 + 1/(3 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009
MAPLE
Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
MATHEMATICA
ContinuedFraction[Sqrt[11], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{3}, 120, {6, 3}] (* Harvey P. Dale, Jan 18 2025 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(11)); for (n=0, 20000, write("b040007.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009
CROSSREFS
KEYWORD
nonn,cofr,easy
AUTHOR
STATUS
approved