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 A040006 Continued fraction for sqrt(10). 10
 3, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Eventual period is (6). - Zak Seidov, Mar 05 2011 The convergents are given in A005667(n+1)/A005668(n+1), n >= 0. - Wolfdieter Lang, Nov 23 2017 LINKS Harry J. Smith, Table of n, a(n) for n = 0..20000 G. Xiao, Contfrac Index entries for linear recurrences with constant coefficients, signature (1). FORMULA a(n) = 6 - 3*(binomial(2*n,n) mod 2), with n>=0. - Paolo P. Lava, Jun 11 2009 a(n) = 3 + 3*sign(n). a(n) = 6, n > 0. - Wesley Ivan Hurt, Nov 01 2013 EXAMPLE 3.162277660168379331998893544... = 3 + 1/(6 + 1/(6 + 1/(6 + 1/(6 + ...)))). MAPLE Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'): MATHEMATICA ContinuedFraction[Sqrt[10], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *) PROG (PARI) allocatemem(932245000); default(realprecision, 33000); x=contfrac(sqrt(10)); for (n=0, 20000, write("b040006.txt", n, " ", x[n+1])); \\ Harry J. Smith, Jun 02 2009 (MAGMA) [6-3*(Binomial(2*n, n) mod 2): n in [0..100]]; // Vincenzo Librandi, Jan 03 2016 CROSSREFS Cf. A010467 (decimal expansion), A005667(n+1)/A005668(n+1). Sequence in context: A113737 A292165 A327576 * A155067 A094011 A295558 Adjacent sequences:  A040003 A040004 A040005 * A040007 A040008 A040009 KEYWORD nonn,cofr,easy AUTHOR STATUS approved

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Last modified October 13 19:52 EDT 2019. Contains 327981 sequences. (Running on oeis4.)