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

0,1

Links

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

Index entries for continued fractions for constants

Index entries for eventually constant sequences.

Index entries for linear recurrences with constant coefficients, signature (1).

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)

Example

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

Maple

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

Mathematica

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

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,...)).

Sequence in context: A195745 A078855 A053430 * A115809 A303698 A164012

Adjacent sequences: A040927 A040928 A040929 * A040931 A040932 A040933

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved