OFFSET
0,1
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 95 at p. 262.
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 (0,0,0,1).
FORMULA
From Amiram Eldar, Nov 12 2023: (Start)
Multiplicative with a(2) = 3, a(2^e) = 8 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 5/4^s). (End)
From Stefano Spezia, Aug 17 2024: (Start)
G.f.: (4 + x + 3*x^2 + x^3 + 4*x^4)/(1 - x^4).
E.g.f.: (5*cos(x) + 11*cosh(x) + 2*sinh(x) - 8)/2. (End)
EXAMPLE
4.795831523312719541597438064... = 4 + 1/(1 + 1/(3 + 1/(1 + 1/(8 + ...)))). - Harry J. Smith, Jun 03 2009
MATHEMATICA
ContinuedFraction[Sqrt[23], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{4}, 120, {8, 1, 3, 1}] (* Harvey P. Dale, Oct 23 2024 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(23)); for (n=0, 20000, write("b010127.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 03 2009
CROSSREFS
KEYWORD
nonn,cofr,easy,mult
AUTHOR
STATUS
approved