OFFSET
0,1
COMMENTS
Decimal expansion of 106/495. - Elmo R. Oliveira, Oct 03 2025
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 (0,1).
FORMULA
From Amiram Eldar, Nov 12 2023: (Start)
Multiplicative with a(2^e) = 4, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 3/2^s). (End)
G.f.: (2 + x + 2*x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025
E.g.f.: 4*cosh(x) + sinh(x) - 2. - Elmo R. Oliveira, Oct 03 2025
EXAMPLE
2.828427124746190097603377448... = 2 + 1/(1 + 1/(4 + 1/(1 + 1/(4 + ...)))). - Harry J. Smith, Jun 02 2009
MAPLE
Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
MATHEMATICA
ContinuedFraction[Sqrt[8], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(8)); for (n=0, 20000, write("b040005.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009
CROSSREFS
KEYWORD
nonn,cofr,easy,mult
AUTHOR
STATUS
approved