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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			16 + 1/(32 + 1/(32 + 1/(32 + 1/(32 + ...)))) = sqrt(257).
		

Links

• Index entries for continued fractions for constants
• Index to divisibility sequences
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A041480/A041481 (convergents).

Cf. A040000, A040002, A040012, A040056.

Programs

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 *)

PARI

a(n)=if(n,32,16) \\ Charles R Greathouse IV, Apr 08 2012

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)