A010721 -id:A010721 - cp's OEIS frontend

A040021 Continued fraction for sqrt(27).

5, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5

Offset: 0

N. J. A. Sloane

			5.1961524227066318805823390... = 5 + 1/(5 + 1/(10 + 1/(5 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010482 (Decimal expansion), A010721.

ContinuedFraction(Sqrt(27)); // G. C. Greubel, Feb 16 2018

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

ContinuedFraction[Sqrt[27],300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{5},120,{10,5}] (* Harvey P. Dale, Jul 19 2015 *)

{ allocatemem(932245000); default(realprecision, 35000); x=contfrac(sqrt(27)); for (n=0, 20000, write("b040021.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

G.f.: 5*(1 + x + x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025

A176325 Decimal expansion of (5+3*sqrt(3))/2.

Original entry on oeis.org

5, 0, 9, 8, 0, 7, 6, 2, 1, 1, 3, 5, 3, 3, 1, 5, 9, 4, 0, 2, 9, 1, 1, 6, 9, 5, 1, 2, 2, 5, 8, 8, 0, 8, 5, 5, 0, 4, 1, 4, 2, 0, 7, 8, 8, 0, 7, 1, 5, 5, 7, 0, 9, 4, 2, 0, 8, 3, 7, 1, 0, 4, 6, 9, 1, 7, 7, 8, 9, 9, 5, 2, 5, 3, 6, 3, 2, 0, 0, 0, 5, 5, 6, 2, 1, 7, 1, 9, 2, 8, 0, 1, 3, 5, 8, 7, 2, 8, 6, 3, 5, 1, 3, 4, 3

Offset: 1

Klaus Brockhaus, Apr 15 2010

Continued fraction expansion of (5+3*sqrt(3))/2 is A010721.

a(n) = A104956(n) for n > 2.

			5.09807621135331594029...

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A002194 (decimal expansion of sqrt(3)), A104956 (decimal expansion of (3*sqrt(3))/2), A010721 (repeat 5, 10).

SetDefaultRealField(RealField(100)); (5+3*Sqrt(3))/2; // G. C. Greubel, Dec 05 2019

evalf( (5+3*sqrt(3))/2, 100); # G. C. Greubel, Dec 05 2019

RealDigits[(5+3Sqrt[3])/2,10,120][[1]] (* Harvey P. Dale, May 20 2011 *)

default(realprecision, 100); (5+3*sqrt(3))/2 \\ G. C. Greubel, Dec 05 2019

numerical_approx((5+3*sqrt(3))/2, digits=100) # G. C. Greubel, Dec 05 2019

A176532 Decimal expansion of 5+3*sqrt(3).

Original entry on oeis.org

1, 0, 1, 9, 6, 1, 5, 2, 4, 2, 2, 7, 0, 6, 6, 3, 1, 8, 8, 0, 5, 8, 2, 3, 3, 9, 0, 2, 4, 5, 1, 7, 6, 1, 7, 1, 0, 0, 8, 2, 8, 4, 1, 5, 7, 6, 1, 4, 3, 1, 1, 4, 1, 8, 8, 4, 1, 6, 7, 4, 2, 0, 9, 3, 8, 3, 5, 5, 7, 9, 9, 0, 5, 0, 7, 2, 6, 4, 0, 0, 1, 1, 1, 2, 4, 3, 4, 3, 8, 5, 6, 0, 2, 7, 1, 7, 4, 5, 7, 2, 7, 0, 2, 6, 8

Offset: 2

Klaus Brockhaus, Apr 24 2010

Continued fraction expansion of 5+3*sqrt(3) is A010721 preceded by 10.

a(n) = A010482(n-2) for n > 3.

			5+3*sqrt(3) = 10.19615242270663188058...

Cf. A002194 (decimal expansion of sqrt(3)), A010482 (decimal expansion of sqrt(27)), A010721 (repeat 5, 10).

RealDigits[5+3Sqrt[3],10,120][[1]] (* Harvey P. Dale, May 30 2012 *)

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A040021 Continued fraction for sqrt(27).

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A176325 Decimal expansion of (5+3*sqrt(3))/2.

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A176532 Decimal expansion of 5+3*sqrt(3).

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