A040930 Continued fraction for sqrt(962).

31, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			31 + 1/(62 + 1/(62 + 1/(62 + 1/(62 + ...)))) = sqrt(962).
		

Links

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

Crossrefs

Cf. A042860/A042861 (convergents).

Continued fraction for sqrt(a^2+1) = (a, 2a, 2a, 2a....): A040000 (contfrac(sqrt(2)) = (1,2,2,...)), A040002, A040006, A040012, A040020, A040030, A040042, A040056, A040072, A040090, A040110 (contfrac(sqrt(122)) = (11,22,22,...)), A040132, A040156, A040182, A040210, A040240, A040272, A040306, A040342, A040380, A040420 (contfrac(sqrt(442)) = (21,42,42,...)), A040462, A040506, A040552, A040600, A040650, A040702, A040756, A040812, A040870 (contfrac(sqrt(901)) = (30,60,60,...)).

Programs

Maple

with(numtheory): Digits := 300: convert(evalf(sqrt(962)),confrac);

Mathematica

PadRight[{31},100,62] (* Harvey P. Dale, Sep 18 2012 *)

Formula

G.f.: 31*(1+x)/(1-x). - Colin Barker, Aug 11 2012

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

a(n) = 62 for n >= 1.

E.g.f.: 62*exp(x) - 31.

a(n) = 31*A040000(n). (End)