A040132 - OEIS

A040132

Continued fraction for sqrt(145).

12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..53.

Index entries for continued fractions for constants

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

FORMULA

From Elmo R. Oliveira, Feb 12 2024: (Start)

a(n) = 24 for n >= 1.

G.f.: 12*(1+x)/(1-x).

E.g.f.: 24*exp(x) - 12.

a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)

EXAMPLE

12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).

MAPLE

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

MATHEMATICA

ContinuedFraction[Sqrt[145], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011*)

CROSSREFS

Cf. A041264/A041265 (convergents), A176910 (decimal expansion).

Cf. A040000, A040002, A040006.

Sequence in context: A075606 A183192 A117320 * A296749 A297276 A095780

Adjacent sequences: A040129 A040130 A040131 * A040133 A040134 A040135

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved