A040756 Continued fraction for sqrt(785).

28, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			28 + 1/(56 + 1/(56 + 1/(56 + 1/(56 + ...)))) = sqrt(785).
		

Links

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

Crossrefs

Cf. A042512/A042513 (convergents).

Cf. A040000, A040002, A040012.

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(785)),confrac);

Mathematica

Block[{$MaxExtraPrecision =1000},ContinuedFraction[Sqrt[785],70]] (* or *) PadRight[{28},70,56] (* Harvey P. Dale, May 09 2012 *)

Formula

From Elmo R. Oliveira, Feb 16 2024: (Start)

a(n) = 56 for n >= 1.

G.f.: 28*(1+x)/(1-x).

E.g.f.: 56*exp(x) - 28.

a(n) = 28*A040000(n) = 14*A040002(n) = 7*A040012(n). (End)