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 A040003 Continued fraction for sqrt(6). 4
 2, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 (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 linear recurrences with constant coefficients, signature (0, 1). FORMULA a(n) = 3 + (-1)^n - 2*(binomial(2*n, n) mod 2), with n >= 0. - Paolo P. Lava, Jun 11 2009 a(n-1) = gcd(2^n, 3^n+1) (empirical). - Michel Marcus, Sep 03 2020 EXAMPLE 2.449489742783178098197284074... = 2 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + ...)))). - Harry J. Smith, Jun 01 2009 MAPLE Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'): MATHEMATICA ContinuedFraction[Sqrt[6], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *) PROG (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(6)); for (n=0, 20000, write("b040003.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 01 2009 (MAGMA) [3+(-1)^n-2*(Binomial(2*n, n) mod 2): n in [0..100]]; // Vincenzo Librandi, Jan 03 2016 CROSSREFS Cf. A010464 (decimal expansion). Equals twice A040001. Sequence in context: A054763 A100374 A045841 * A106469 A082508 A327730 Adjacent sequences:  A040000 A040001 A040002 * A040004 A040005 A040006 KEYWORD nonn,cofr,easy AUTHOR STATUS approved

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Last modified December 4 21:58 EST 2020. Contains 338941 sequences. (Running on oeis4.)