OFFSET
0,1
COMMENTS
Eventual period is (6). - Zak Seidov, Mar 05 2011
Decimal expansion of 11/30. - Elmo R. Oliveira, Feb 16 2024
REFERENCES
Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.
James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
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) = 3 + 3*sign(n). a(n) = 6, n > 0. - Wesley Ivan Hurt, Nov 01 2013
From Elmo R. Oliveira, Feb 16 2024: (Start)
G.f.: 3*(1+x)/(1-x).
E.g.f.: 6*exp(x) - 3.
a(n) = 3*A040000(n). (End)
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 *)
PadRight[{3}, 120, {6}] (* Harvey P. Dale, Aug 25 2024 *)
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
KEYWORD
nonn,cofr,easy
AUTHOR
STATUS
approved