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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 Harry J. Smith, Table of n, a(n) for n = 0..20000 G. Xiao, Contfrac. Index entries for continued fractions for constants. Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). 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 Adjacent sequences: A010128 A010129 A010130 * A010132 A010133 A010134 KEYWORD nonn,cofr,easy,mult AUTHOR N. J. A. Sloane STATUS approved

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