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A040030
Continued fraction for sqrt(37).
5
6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
OFFSET
0,1
FORMULA
From Elmo R. Oliveira, Feb 06 2024: (Start)
a(n) = 12 for n >= 1.
G.f.: 6*(1+x)/(1-x).
E.g.f.: 12*exp(x) - 6.
a(n) = 6*A040000(n) = 3*A040002(n) = 2*A040006(n). (End)
EXAMPLE
6.08276253029821968899968... = 6 + 1/(12 + 1/(12 + 1/(12 + 1/(12 + ...)))). - Harry J. Smith, Jun 04 2009
MAPLE
Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
MATHEMATICA
ContinuedFraction[Sqrt[37], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{6}, 120, {12}] (* Harvey P. Dale, Jan 02 2017 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 44000); x=contfrac(sqrt(37)); for (n=0, 20000, write("b040030.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009
CROSSREFS
Cf. A010491 (decimal expansion), A041060/A041061 (convergents), A248263 (Egyptian fraction).
Sequence in context: A060479 A028998 A285057 * A315567 A315568 A315569
KEYWORD
nonn,cofr,easy
STATUS
approved