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A040132
Continued fraction for sqrt(145).
5
12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
OFFSET
0,1
FORMULA
From Elmo R. Oliveira, Feb 12 2024: (Start)
a(n) = 24 for n >= 1.
G.f.: 12*(1+x)/(1-x).
E.g.f.: 24*exp(x) - 12.
a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)
EXAMPLE
12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).
MAPLE
Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
MATHEMATICA
ContinuedFraction[Sqrt[145], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011*)
CROSSREFS
Cf. A041264/A041265 (convergents), A176910 (decimal expansion).
Sequence in context: A075606 A183192 A117320 * A296749 A297276 A095780
KEYWORD
nonn,cofr,easy
AUTHOR
STATUS
approved