A002945 -id:A002945 - cp's OEIS frontend

A268515 Records in A002945 (continued fraction expansion of cube root of 2).

1, 3, 5, 8, 14, 15, 534, 7451, 12737, 22466, 68346, 148017, 217441, 320408, 533679, 4156269, 4886972, 10253793, 13761184, 14358891, 35950987, 68665026, 455880544, 10065016098

Offset: 1

N. J. A. Sloane, Feb 07 2016, following a suggestion from Doron Zeilberger

a(1)-a(18) computed by John M. Campbell, Oct 23 2010 (cf. A181495).

It is not known if this sequence is infinite (i.e., whether the continued fraction expansion is bounded). [Davenport]

H. Davenport, The Higher Arithmetic: An Introduction to the Theory of Numbers, Cambridge, 2008.

Cf. A002945, A181495 (positions of records).

a(19)-a(21) from Zak Seidov, Feb 08 2016
a(22)-a(24) from Hans Havermann, Feb 08 2016
Name corrected by Nathan Fox, Feb 08 2016

A002580 Decimal expansion of cube root of 2.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

2^(1/3) is Hermite's constant gamma_3. - Jean-François Alcover, Sep 02 2014, after Steven Finch.
For doubling the cube using origami and a standard geometric construction employing two right angles see the W. Lang link, Application 2, p. 14, and the references given there. See also the L. Newton link. - Wolfdieter Lang, Sep 02 2014
Length of an edge of a cube with volume 2. - Jared Kish, Oct 16 2014
For any positive real c, the mappings R(x)=(c*x)^(1/4) and S(x)=sqrt(c/x) have the same unique attractor c^(1/3), to which their iterated applications converge from any complex plane point. The present case is obtained setting c=2. It is noteworthy that in this way one can evaluate cube roots using only square roots. The CROSSREFS list some other cases of cube roots to which this comment might apply. - Stanislav Sykora, Nov 11 2015
The cube root of any positive number can be connected to the Philo lines (or Philon lines) for a 90-degree angle. If the equation x^3-2 is represented using Lill's method, it can be shown that the path of the root 2^(1/3) creates the shortest segment (Philo line) from the x axis through (1,2) to the y axis. For more details see the article "Lill's method and the Philo Line for Right Angles" linked below. - Raul Prisacariu, Apr 06 2024

			1.2599210498948731647672106072782283505702514...

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See pp. 192-193.
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §3.4 Irrational Numbers and §12.3 Euclidean Construction, pp. 84, 421.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Horace S. Uhler, Many-figure approximations for cubed root of 2, cubed root of 3, cubed root of 4, and cubed root of 9 with chi2 data. Scripta Math. 18, (1952). 173-176.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, pp. 33-34.

Harry J. Smith, Table of n, a(n) for n = 1..20000
Laszlo C. Bardos, Double a Cube, CutOutFoldUp.
Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 62.
Wolfdieter Lang, Notes on Some Geometric and Algebraic Problems solved by Origami, arXiv:1409.4799 [math.MG], 2014.
Liz Newton, The power of origami.
Raul Prisacariu, Lill's method and the Philo Line for Right Angles.
Simon Plouffe, Plouffe's Inverter, The cube root of 2 to 20000 digits.
Simon Plouffe, 2**(1/3) to 2000 places.
Simon Plouffe, Generalized expansion of real constants.
H. S. Uhler, Many-figure approximations for cubed root of 2, cubed root of 3, cubed root of 4, and cubed root of 9 with chi2 data, Scripta Math. 18, (1952). 173-176. [Annotated scanned copies of pages 175 and 176 only]
Eric Weisstein's World of Mathematics, Delian Constant.
Index entries for algebraic numbers, degree 3.

Cf. A002945 (continued fraction), A270714 (reciprocal), A253583.
Cf. A246644.
Cf. A002581, A005480, A005481, A005482, A005486, A010581, A010582, A092039, A092041, A139340.

Digits:=100: evalf(2^(1/3)); # Wesley Ivan Hurt, Nov 12 2015

RealDigits[N[2^(1/3), 5!]] (* Vladimir Joseph Stephan Orlovsky, Sep 04 2008 *)

default(realprecision, 20080); x=2^(1/3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002580.txt", n, " ", d));  \\ Harry J. Smith, May 07 2009

default(realprecision, 100); x= 2^(1/3); for(n=1, 100, d=floor(x); x=(x-d)*10; print1(d, ", "))  \\ Altug Alkan, Nov 14 2015

(-2^(1/3) - 2^(1/3) * sqrt(-3))^3 = (-2^(1/3) + 2^(1/3) * sqrt(-3))^3 = 16. - Alonso del Arte, Jan 04 2015
Set c=2 in the identities c^(1/3) = sqrt(c/sqrt(c/sqrt(c/...))) = sqrt(sqrt(c*sqrt(sqrt(c*sqrt(sqrt(...)))))). - Stanislav Sykora, Nov 11 2015
Equals Product_{k>=0} (1 + (-1)^k/(3*k + 2)). - Amiram Eldar, Jul 25 2020
From Peter Bala, Mar 01 2022: (Start)
Equals Sum_{n >= 0} (1/(3*n+1) - 1/(3*n-2))*binomial(1/3,n) = (3/2)* hypergeom([-1/3, -2/3], [4/3], -1). Cf. A290570.
Equals 4/3 - 4*Sum_{n >= 1} binomial(1/3,2*n+1)/(6*n-1) = (4/3)*hypergeom ([1/2, -1/6], [3/2], 1).
Equals hypergeom([-2/3, -1/6], [1/2], 1).
Equals hypergeom([2/3, 1/6], [4/3], 1). (End)

A039921 Continued fraction expansion of w = 2*cos(Pi/7).

Original entry on oeis.org

1, 1, 4, 20, 2, 3, 1, 6, 10, 5, 2, 2, 1, 2, 2, 1, 18, 1, 1, 3, 2, 1, 2, 1, 2, 1, 39, 2, 1, 1, 1, 13, 1, 2, 1, 30, 1, 1, 1, 3, 2, 5, 4, 1, 5, 1, 5, 1, 2, 1, 1, 94, 6, 2, 19, 11, 1, 60, 1, 1, 50, 2, 1, 1, 8, 53, 1, 3, 1, 6, 3, 2, 1, 5, 1, 1, 3, 4, 636, 1, 2, 1, 3, 3, 7, 9, 1, 2, 10, 3, 1, 22, 1, 119, 3

Offset: 0

N. J. A. Sloane

Arises in the approximation of 14-fold quasipatterns by 14 Fourier modes.

			w = 1.80193773580483825247220463901489010233183832426371430010712484639886...
Equals 1 + 1/(1 + 1/(4 + 1/(20 + 1/(2 + ...)))). - _Harry J. Smith_, May 31 2009

A. M. Rucklidge & W. J. Rucklidge (preprint) 2002.

Harry J. Smith, Table of n, a(n) for n = 0..20000
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
Alastair Rucklidge, Home page
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A160389 (Decimal expansion). - Harry J. Smith, May 31 2009

Mathematica
```
ContinuedFraction[2*Cos[Pi/7], 100]
```

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(2*cos(Pi/7)); for (n=0, 20000, write("b039921.txt", n, " ", x[n+1])); } \\ Harry J. Smith, May 31 2009

w satisfies w^3 - w^2 - 2w + 1 = 0 and so is algebraic.

The other two roots are 2*cos(3 Pi/7) and 2*cos(5 Pi/7); their continued fraction expansions also end in 20, 2, 3, 1, 6, 10, 5, 2, 2, 1, ... which is a(n) for n >= 3. - Greg Dresden, Jul 01 2018

A002351 Denominators of convergents to cube root of 2.

Original entry on oeis.org

1, 3, 4, 23, 27, 50, 227, 277, 504, 4309, 4813, 71691, 76504, 836731, 1749966, 2586697, 12096754, 147747745, 307592244, 1070524477, 2448641198, 3519165675, 13006138223, 55543718567, 68549856790, 124093575357, 316737007504

Offset: 0

N. J. A. Sloane

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.
P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Robert Israel, Table of n, a(n) for n = 0..1975
E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers, In: Bosma W., van der Poorten A. (eds) Computational Algebra and Number Theory. Mathematics and Its Applications, vol 325.
E. B. Burger, Diophantine Olympics and World Champions: Polynomials and Primes Down Under, Amer. Math. Monthly, 107 (Nov. 2000), 822-829.

Cf. A002352 (numerators), A002945.

Digits := 60: E := 2^(1/3); convert(evalf(E),confrac,50,'cvgts'): cvgts;
# Alternate:
N:= 100: # to get a(1) to a(N)
c[0] := 1: p[0] := 1: a[0] := 0: p[1] := 1: a[1] := 1:
for n from 1 to N do
  c[n] := floor((-1)^(n)*3*p[n]^2/(a[n]*(p[n]^3-2*a[n]^3)) - a[n-1]/a[n]);
  p[n+1] := c[n]*p[n] + p[n-1];
  a[n+1] := c[n]*a[n] + a[n-1];
od:
seq(a[i], i=1..N); # Robert Israel, Oct 08 2017

Denominator[Convergents[Surd[2,3],30]] (* Harvey P. Dale, Apr 02 2018 *)

Offset changed by Andrew Howroyd, Jul 04 2024

A002352 Numerators of convergents to cube root of 2.

Original entry on oeis.org

1, 4, 5, 29, 34, 63, 286, 349, 635, 5429, 6064, 90325, 96389, 1054215, 2204819, 3259034, 15240955, 186150494, 387541943, 1348776323, 3085094589, 4433870912, 16386707325, 69980700212, 86367407537, 156348107749, 399063623035, 5743238830239, 17628780113752

Offset: 0

N. J. A. Sloane

D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 67.
P. Seeling, Verwandlung der irrationalen Groesse ... in einen Kettenbruch, Archiv. Math. Phys., 46 (1866), 80-120.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Robert Israel, Table of n, a(n) for n = 0..1975
E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers, In: Bosma W., van der Poorten A. (eds) Computational Algebra and Number Theory. Mathematics and Its Applications, vol 325.
E. B. Burger, Diophantine Olympics and World Champions: Polynomials and Primes Down Under, Amer. Math. Monthly, 107 (Nov. 2000), 822-829.

Cf. A002351 (denominators), A002945.

Digits := 60: E := 2^(1/3); convert(evalf(E),confrac,50,'cvgts'): cvgts;
# Alternate:
N:= 100: # to get a(1) to a(N)
c[0] := 1: a[0] := 1: q[0] := 0: a[1] := 1: q[1] := 1:
for n from 1 to N do
  c[n] := floor((-1)^n*3*a[n]^2/(q[n]*(a[n]^3-2*q[n]^3)) - q[n-1]/q[n]);
  a[n+1] := c[n]*a[n] + a[n-1];
  q[n+1] := c[n]*q[n] + q[n-1];
od: seq(a[i], i=1..N); # Robert Israel, Oct 08 2017

Convergents[CubeRoot[2],30]//Numerator (* Harvey P. Dale, May 30 2023 *)

From Robert Israel, Oct 08 2017: (Start)
c(n) = floor((-1)^n*3*a(n)^2/(q(n)*(a(n)^3-2*q(n)^3)) - q(n-1)/q(n)),
a(n+1) = c(n)*a(n) + a(n-1),
q(n+1) = c(n)*q(n) + q(n-1), with a(0) = 1, c(0) = 1, q(0) = 0, a(1) = 1, q(1) = 1. (End)

Offset changed by Andrew Howroyd, Jul 04 2024

A005483 Continued fraction for cube root of 7.

Original entry on oeis.org

1, 1, 10, 2, 16, 2, 1, 4, 2, 1, 21, 1, 3, 5, 1, 2, 1, 1, 2, 11, 5, 1, 3, 1, 2, 27, 4, 1, 282, 8, 1, 2, 1, 1, 3, 1, 3, 2, 6, 4, 1, 2, 1, 5, 1, 1, 2, 1, 1, 1, 3, 2, 8, 1, 2, 2, 4, 5, 1, 1, 36, 1, 1, 1, 1, 2, 1, 2, 31, 2, 1, 1, 7, 1, 1, 1, 1, 6, 7, 6, 5, 7, 1, 6, 1

Offset: 0

N. J. A. Sloane

			7^(1/3) = 1.912931182772389... = 1 + 1/(1 + 1/(10 + 1/(2 + 1/(16 + ...)))). - _Harry J. Smith_, May 08 2009

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harry J. Smith, Table of n, a(n) for n = 0..19999
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A005482 (decimal expansion).

Cf. A005484, A005485 (convergents).

ContinuedFraction[Surd[7,3],70] (* Harvey P. Dale, Oct 01 2013 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(7^(1/3)); for (n=1, 20000, write("b005483.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

Offset changed by Andrew Howroyd, Jul 05 2024

A002946 Continued fraction for cube root of 3.

Original entry on oeis.org

1, 2, 3, 1, 4, 1, 5, 1, 1, 6, 2, 5, 8, 3, 3, 4, 2, 6, 4, 4, 1, 3, 2, 3, 4, 1, 4, 9, 1, 8, 4, 3, 1, 3, 2, 6, 1, 6, 1, 3, 1, 1, 1, 1, 12, 3, 1, 3, 1, 1, 4, 1, 6, 1, 5, 1, 2, 1, 3, 3, 11, 8, 1, 139, 8, 2, 8, 5, 1, 2, 2, 2, 2, 3, 1, 1, 2, 1, 1, 1, 52, 2, 46, 2, 2, 3

Offset: 0

N. J. A. Sloane

			3^(1/3) = 1.44224957030740838... = 1 + 1/(2 + 1/(3 + 1/(1 + 1/(4 + ...)))). - _Harry J. Smith_, May 08 2009

H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harry J. Smith, Table of n, a(n) for n = 0..19999
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A002581 (decimal expansion).

Cf. A002353, A002354 (convergents).

SetDefaultRealField(RealField(100)); ContinuedFraction(3^(1/3)); // G. C. Greubel, Nov 02 2018

with(numtheory): cfrac(3^(1/3),80,'quotients'); # Muniru A Asiru, Nov 02 2018

ContinuedFraction[Power[3, (3)^-1],120] (* Harvey P. Dale, May 11 2011 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(3^(1/3)); for (n=1, 20000, write("b002946.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

Offset changed by Andrew Howroyd, Jul 04 2024

A002947 Continued fraction for cube root of 4.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 3, 2, 3, 1, 3, 1, 30, 1, 4, 1, 2, 9, 6, 4, 1, 1, 2, 7, 2, 3, 2, 1, 6, 1, 1, 1, 25, 1, 7, 7, 1, 1, 1, 1, 266, 1, 3, 2, 1, 3, 60, 1, 5, 1, 8, 5, 6, 1, 4, 20, 1, 4, 1, 1, 14, 1, 4, 4, 1, 1, 1, 1, 7, 3, 1, 1, 2, 1, 3, 1, 4, 4, 1, 1, 1, 3, 1, 34, 8, 2, 10, 6, 3, 1, 2, 31, 1, 1, 1, 4, 3, 44, 1, 45

Offset: 0

N. J. A. Sloane

			4^(1/3) = 1.58740105196819947... = 1 + 1/(1 + 1/(1 + 1/(2 + 1/(2 + ...)))). - _Harry J. Smith_, May 08 2009

H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harry J. Smith, Table of n, a(n) for n = 0..19999
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
Gang Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A005480 (decimal expansion). - Harry J. Smith, May 08 2009

Cf. A002355, A002356 (convergents).

[ContinuedFraction(4^(1/3))]; // Vincenzo Librandi, Aug 02 2015

ContinuedFraction[4^(1/3), 80] (* Alonso del Arte, Jul 24 2015 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(4^(1/3)); for (n=1, 20000, write("b002947.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003

Offset changed by Andrew Howroyd, Jul 04 2024

A002948 Continued fraction for cube root of 5.

Original entry on oeis.org

1, 1, 2, 2, 4, 3, 3, 1, 5, 1, 1, 4, 10, 17, 1, 14, 1, 1, 3052, 1, 1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 1, 13, 5, 1, 1, 1, 13, 2, 41, 1, 4, 12, 1, 5, 2, 7, 1, 1, 3, 33, 2, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 15, 12, 8, 10, 48, 1, 2, 1, 1, 3, 4, 1, 474, 1, 13, 2, 4, 1, 1, 49

Offset: 0

N. J. A. Sloane

			5^(1/3) = 1.70997594667669698... = 1 + 1/(1 + 1/(2 + 1/(2 + 1/(4 + ...)))). - _Harry J. Smith_, May 08 2009

H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Harry J. Smith, Table of n, a(n) for n = 0..19999
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134.
S. Lang and H. Trotter, Continued fractions for some algebraic numbers, J. Reine Angew. Math. 255 (1972), 112-134. [Annotated scanned copy]
Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A005481 (decimal expansion).

Cf. A002357, A002358 (convergents).

SetDefaultRealField(RealField(100)); ContinuedFraction(5^(1/3)); // G. C. Greubel, Nov 02 2018

with(numtheory): cfrac(5^(1/3),80,'quotients'); # Muniru A Asiru, Nov 02 2018

ContinuedFraction[5^(1/3), 100] (* G. C. Greubel, Nov 02 2018 *)

{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/3)); for (n=1, 20000, write("b002948.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 08 2009

Offset changed by Andrew Howroyd, Jul 04 2024

A179613 Continued fraction for 2^(1/4).

Original entry on oeis.org

1, 5, 3, 1, 1, 40, 5, 1, 1, 25, 2, 3, 1, 6, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 7, 2, 7, 1, 1, 1, 2, 1, 1, 32, 4, 1, 6, 2, 1, 1, 1, 15, 1, 5, 1, 4, 1, 1, 1, 3, 1, 3, 7, 2, 7, 1, 1, 3, 31, 1, 3, 1, 3, 1, 9, 18, 4, 5, 3, 1, 2, 3, 2, 1, 3, 7, 1, 3, 1, 9, 10, 2, 1, 2, 1, 14, 1, 17, 1, 2, 2, 1, 7, 1, 5, 3, 14, 1

Offset: 0

Vladimir Joseph Stephan Orlovsky, Jul 20 2010

2^(1/4) = 1.1892071150027210667174999705604759152929720...

Cf. A010767 (decimal expansion), A002945.

Mathematica
```
ContinuedFraction[2^(1/4),200]
```

Offset changed by Andrew Howroyd, Jul 07 2024

cp's OEIS Frontend

A268515 Records in A002945 (continued fraction expansion of cube root of 2).

Views

Author

Keywords

Comments

References

Crossrefs

Extensions

A002580 Decimal expansion of cube root of 2.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Maple

Mathematica

PARI

PARI

Formula

A039921 Continued fraction expansion of w = 2*cos(Pi/7).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A002351 Denominators of convergents to cube root of 2.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A002352 Numerators of convergents to cube root of 2.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Maple

Mathematica

Formula

Extensions

A005483 Continued fraction for cube root of 7.

Views

Author

Keywords

Examples

References

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A002946 Continued fraction for cube root of 3.

Views

Author

Keywords

Examples

References

Links

Crossrefs