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A040420
Continued fraction for sqrt(442).
4
21, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42
OFFSET
0,1
FORMULA
From Elmo R. Oliveira, Feb 15 2024: (Start)
a(n) = 42 for n >= 1.
G.f.: 21*(1+x)/(1-x).
E.g.f.: 42*exp(x) - 21.
a(n) = 21*A040000(n) = 7*A040006(n) = 3*A040042(n). (End)
EXAMPLE
21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).
MAPLE
with(numtheory): Digits := 300: convert(evalf(sqrt(442)), confrac);
CROSSREFS
Cf. A041840/A041841 (convergents).
Sequence in context: A362849 A120772 A260749 * A192130 A258188 A037978
KEYWORD
nonn,cofr,easy,less
STATUS
approved