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A010131 Continued fraction for sqrt(33). 3
5, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10, 1, 2, 1, 10 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
G. Xiao, Contfrac.
FORMULA
From Amiram Eldar, Nov 12 2023: (Start)
Multiplicative with a(2) = 2, a(2^e) = 10 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 1/2^(2*s-3) + 1/2^s). (End)
EXAMPLE
5.74456264653802865985061146... = 5 + 1/(1 + 1/(2 + 1/(1 + 1/(10 + ...)))). - Harry J. Smith, Jun 04 2009
MATHEMATICA
ContinuedFraction[Sqrt[33], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
LinearRecurrence[{0, 0, 0, 1}, {5, 1, 2, 1, 10}, 100] (* or *) PadRight[{5}, 100, {10, 1, 2, 1}] (* Harvey P. Dale, Dec 31 2017 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(33)); for (n=0, 20000, write("b010131.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009
CROSSREFS
Cf. A010488 (decimal expansion).
Sequence in context: A115038 A231990 A369915 * A176323 A260821 A068115
KEYWORD
nonn,cofr,easy,mult
AUTHOR
STATUS
approved

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Last modified July 20 06:10 EDT 2024. Contains 374441 sequences. (Running on oeis4.)