A040420 Continued fraction for sqrt(442).

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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• less

Examples

			21 + 1/(42 + 1/(42 + 1/(42 + 1/(42 + ...)))) = sqrt(442).
		

Links

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

Crossrefs

Cf. A041840/A041841 (convergents).

Cf. A040000, A040006, A040042.

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(442)),confrac);

Mathematica

Block[{$MaxExtraPrecision=1000}, ContinuedFraction[Sqrt[442],120]] (* or *) PadRight[{21},120,{42}] (* Harvey P. Dale, Nov 28 2024 *)

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)