A040240 Continued fraction for sqrt(257).

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

Links

Table of n, a(n) for n=0..62.

Index entries for continued fractions for constants

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (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).

Cf. A040000, A040002, A040012, A040056.

Sequence in context: A132299 A240053 A059164 * A296761 A297288 A335246

Adjacent sequences: A040237 A040238 A040239 * A040241 A040242 A040243

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved