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A040012
Continued fraction for sqrt(17).
13
4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
OFFSET
0,1
COMMENTS
Decimal expansion of 22/45. - Elmo R. Oliveira, Feb 06 2024
REFERENCES
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง4.4 Powers and Roots, p. 144.
FORMULA
a(n) = 4*A040000(n). - Stefano Spezia, May 14 2023
From Elmo R. Oliveira, Feb 06 2024: (Start)
a(n) = 8 for n >= 1.
G.f.: 4*(1+x)/(1-x).
E.g.f.: 8*exp(x) - 4. (End)
EXAMPLE
4.123105625617660549821409855... = 4 + 1/(8 + 1/(8 + 1/(8 + 1/(8 + ...)))). - Harry J. Smith, Jun 03 2009
MAPLE
Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
MATHEMATICA
ContinuedFraction[Sqrt[17], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 100, 8] (* Harvey P. Dale, Jun 22 2015 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 37000); x=contfrac(sqrt(17)); for (n=0, 20000, write("b040012.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009
CROSSREFS
Cf. A041024/A041025 (convergents), A010473 (decimal expansion), A248245 (Egyptian fraction).
Cf. A040000.
Sequence in context: A200357 A201405 A331067 * A054006 A029679 A304651
KEYWORD
nonn,cofr,easy
STATUS
approved