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A010169
Continued fraction for sqrt(98).
2
9, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18, 1, 8, 1, 18
OFFSET
0,1
FORMULA
From Wesley Ivan Hurt, Jun 23 2021: (Start)
a(n) = a(n-4).
a(0) = 9; a(n) = 7 + 6*(-1)^n + 5*cos(n*Pi/2) for n > 0. (End)
From Amiram Eldar, Nov 14 2023: (Start)
Multiplicative with a(2) = 8, a(2^e) = 18 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 7/2^s + 5/2^(2*s-1)). (End)
EXAMPLE
9.89949493661166534161182106... = 9 + 1/(1 + 1/(8 + 1/(1 + 1/(18 + ...)))). - Harry J. Smith, Jun 12 2009
MATHEMATICA
ContinuedFraction[Sqrt[98], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2011 *)
PadRight[{9}, 120, {18, 1, 8, 1}] (* Harvey P. Dale, Dec 13 2015 *)
PROG
(PARI) { allocatemem(932245000); default(realprecision, 24000); x=contfrac(sqrt(98)); for (n=0, 20000, write("b010169.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 12 2009
CROSSREFS
Cf. A010549 (decimal expansion).
Sequence in context: A371856 A182494 A065444 * A113657 A098783 A234468
KEYWORD
nonn,cofr,easy,mult
STATUS
approved