The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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) contfrac(sqrt(10)) \\ For illustration. (PARI) A040006(n)=if(n, 6, 3) \\ M. F. Hasler, Nov 02 2019 (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) (convergents). Sequence in context: A292165 A327576 A331058 * A155067 A094011 A295558 Adjacent sequences:  A040003 A040004 A040005 * A040007 A040008 A040009 KEYWORD nonn,cofr,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 26 21:08 EDT 2020. Contains 338027 sequences. (Running on oeis4.)