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A010170
Continued fraction for sqrt(99).
3
9, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1, 18, 1
OFFSET
0,1
FORMULA
a(n+1) = 18^n mod 19, for all n >= 0. - M. F. Hasler, Mar 10 2011
From Amiram Eldar, Nov 14 2023: (Start)
Multiplicative with a(2^e) = 18, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 17/2^s). (End)
EXAMPLE
9.9498743710661995473447982... = 9 + 1/(1 + 1/(18 + 1/(1 + 1/(18 + ...)))). - Harry J. Smith, Jun 12 2009
MATHEMATICA
ContinuedFraction[Sqrt[99], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9}, 120, {18, 1}] (* Harvey P. Dale, Aug 30 2021 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(99)); for (n=0, 20000, write("b010170.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 12 2009
CROSSREFS
Cf. A010550 (decimal expansion).
Sequence in context: A014721 A054018 A342637 * A317051 A013616 A205381
KEYWORD
nonn,cofr,easy,mult
STATUS
approved