OFFSET
0,1
COMMENTS
Eventual period is (1, 1, 1, 1, 6). - Zak Seidov, Mar 05 2011
Decimal expansion of 311113/999990. - Elmo R. Oliveira, Oct 14 2025
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 96 at p. 264.
Florian Cajori, A History of Mathematical Notations, Dover edition (2012), par. 428.
Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.
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 (0,0,0,0,1).
FORMULA
From Amiram Eldar, Nov 12 2023: (Start)
Multiplicative with a(5^e) = 6, and a(p^e) = 1 for p != 5.
Dirichlet g.f.: zeta(s) * (1 + 1/5^(s-1)). (End)
G.f.: (3 + x + x^2 + x^3 + x^4 + 3*x^5)/(1 - x^5). - Stefano Spezia, Aug 17 2024
EXAMPLE
3.605551275463989293119221267... = 3 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - Harry J. Smith, Jun 02 2009
MATHEMATICA
ContinuedFraction[Sqrt[13], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 13000); x=contfrac(sqrt(13)); for (n=0, 20000, write("b010122.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009
CROSSREFS
KEYWORD
nonn,cofr,easy,mult
AUTHOR
STATUS
approved