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A040240
Continued fraction for sqrt(257).
4
16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32
OFFSET
0,1
FORMULA
From Elmo R. Oliveira, Feb 13 2024: (Start)
a(n) = 32 for n >= 1.
G.f.: 16*(1+x)/(1-x).
E.g.f.: 32*exp(x) - 16.
a(n) = 16*A040000(n) = 8*A040002(n) = 4*A040012(n) = 2*A040056(n). (End)
EXAMPLE
16 + 1/(32 + 1/(32 + 1/(32 + 1/(32 + ...)))) = sqrt(257).
MAPLE
with(numtheory): Digits := 300: convert(evalf(sqrt(257)), confrac);
MATHEMATICA
Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[257], 100]] (* or *) PadRight[{16}, 100, {32}] (* Harvey P. Dale, Aug 15 2021 *)
PROG
(PARI) a(n)=if(n, 32, 16) \\ Charles R Greathouse IV, Apr 08 2012
CROSSREFS
Cf. A041480/A041481 (convergents).
Sequence in context: A132299 A240053 A059164 * A296761 A297288 A335246
KEYWORD
nonn,cofr,easy
STATUS
approved