A002580 -id:A002580 - cp's OEIS frontend

A129702 Egyptian Fraction representation for the cube root of 2.

4, 101, 49851, 56419367438, 7536786358882281953021, 279453545463148713995835426751302046086542901, 530839145233037240327467358793620164059337117424267397603880062554963096104836195587116482

Offset: 1

Jonathan Wellons (wellons(AT)gmail.com), Aug 18 2007

Generated with Perl's BigFloat library. Number of digits in terms is as follows: 1, 3, 5, 11, 22, 45, 90, 182, 363, 726, 1453, 2905...

			Fractional part of 2^(1/3) = 1/4 + 1/101 + 1/49851 + ...

Amiram Eldar, Table of n, a(n) for n = 1..10
Eric Weisstein's World of Mathematics, Egyptian Fraction.
Index entries for sequences related to Egyptian fractions.

Cf. A002580.

A010466 Decimal expansion of square root of 8.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

Sqrt(8) = 2*sqrt(2) is the length of the longest (rigid) ladder that can be carried horizontally around a right angled corner in a hallway of unit width. - Lekraj Beedassy, Apr 19 2006
Continued fraction expansion is 2 followed by {1, 4} repeated. - Harry J. Smith, Jun 05 2009
This is the second Lagrange number. - Alonso del Arte, Dec 06 2011
Also 2*sqrt(2) is the ratio of the perimeter of a square to its diameter (diagonal length). - Rick L. Shepherd, Dec 29 2016
Uchiyama shows that every interval (n, n + c*n^(1/4)) contains an integer that is the sum of two squares, where c = 2^(3/2). - Michel Marcus, Jan 03 2018
This is the area of the eighth-smallest triangle with integer side lengths (2, 3, 3), or the seventh-smallest triangle if two smaller triangles with the same area are counted only once (see A331251). - Hugo Pfoertner, Feb 12 2020
Diameter of a sphere whose surface area equals 8*Pi. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - Omar E. Pol, Feb 13 2020
Sqrt(8) = area between the curves y = sin(x) and y = cos(x) for Pi/4 < x < 5 Pi/4; this is one of infinitely many congruent convex regions bounded by the two curves. - Clark Kimberling, May 03 2020
Area of the regular 8-gon with circumradius =1. - R. J. Mathar, Aug 24 2023

			2.828427124746190097603377448419396157139343750753896146353359475981464...
Sqrt(8) = sqrt(1+2*i*sqrt(2)) + sqrt(1-2*i*sqrt(2)) = sqrt(1/2+2*i*sqrt(3)) + sqrt(1/2-2*i*sqrt(3)), where i=sqrt(-1). - _Bruno Berselli_, Nov 20 2012
1 + 3/4 + 3*5/(4*8) + 3*5*7/(4*8*12) + 3*5*7*9/(4*8*12*16) + ... - _Bruno Berselli_, Mar 16 2014

John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 187.
S. R. Finch, Moving Sofa Constant, Sect. 8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.

Harry J. Smith, Table of n, a(n) for n = 1..20000
Jason Kimberley, Index of expansions of sqrt(d) in base b
R. J. Nemiroff & J. Bonnell, The first 1 million digits of the square root of 8
R. J. Nemiroff & J. Bonnell, Plouffe's Inverter, The first 1 million digits of the square root of 8
Ana Rechtman, Juin 2023, 3e défi, Images des Mathématiques, CNRS, 2023.
S. Uchiyama, On the distribution of integers representable as a sum of two h-th powers, J. Fac. Sci. Hokkaido Univ. Ser. I, 18, 124-127, 1964/1965.
Eric Weisstein's World of Mathematics, Moving Ladder Problem
Index entries for algebraic numbers, degree 2

Cf. A040005 (continued fraction).

Cf. A331250, A331251.

SetDefaultRealField(RealField(100)); Sqrt(8); // Vincenzo Librandi, Feb 13 2020

evalf(2^(3/2)) ; # R. J. Mathar, Jul 15 2013

RealDigits[N[Sqrt[8],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)

default(realprecision, 20080); x=sqrt(8); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010466.txt", n, " ", d));  \\ Harry J. Smith, Jun 02 2009

Equals 1 + Sum_{n>=1} ( Product_{k=1..n} (2k+1)/(4k) ). - Bruno Berselli, Mar 16 2014
Equals 2*A002193. - R. J. Mathar, Jan 14 2021
From Peter Bala, Mar 01 2022: (Start)
Equals 3*Sum_{n >= 0} (1/(4*n+1) - 1/(4*n-3))*binomial(1/2,n). Cf. A002580 and A175576.
Equals 4*hypergeom([-1/2, -3/4], [5/4], -1). (End)
Equals 8 * A020765. - R. J. Mathar, Aug 24 2023

A017979 Powers of cube root of 2 rounded down.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50, 64, 80, 101, 128, 161, 203, 256, 322, 406, 512, 645, 812, 1024, 1290, 1625, 2048, 2580, 3250, 4096, 5160, 6501, 8192, 10321, 13003, 16384, 20642, 26007, 32768, 41285, 52015, 65536, 82570, 104031

Offset: 0

N. J. A. Sloane

nonn

Rounding has no effect when n is a multiple of 3, because then obviously (2^(1/3))^n = 2^(n/3). - Alonso del Arte, Jan 04 2014

			a(2) = 1 because the cube root of 2 squared is 1.5874...
a(3) = 2 because the cube root of 2 cubed is 2 exactly.
a(4) = 2 because the cube root of 2 to the fourth power is 2.519842...

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A017981, A002580.

Sequences of the type: Powers of cube root of (k) rounded down: this sequence (k=2), A017982 (k=3), A017985 (k=4), A017988 (k=5), A017991 (k=6), A017994 (k=7), A018000 (k=9), A018003 (k=10), A018006 (k=11), A018009 (k=12), A018012 (k=13), A018015 (k=14), A018018 (k=15), A018021 (k=16), A018024 (k=17), A018027 (k=18), A018030 (k=19), A018033 (k=20), A018036 (k=21), A018039 (k=22), A018042 (k=23), A018045 (k=24).

[Floor(2^(n/3)): n in [0..50]]; // Vincenzo Librandi, Jan 06 2014

Table[Floor[(2^(1/3))^n], {n, 0, 49}] (* Alonso del Arte, Jan 04 2014 *)

from sympy import integer_nthroot
def A017979(n): return integer_nthroot(1<Chai Wah Wu, Jun 18 2024

a(44)-a(50) from Alex Ratushnyak, Jan 04 2014

A002581 Decimal expansion of cube root of 3.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

The largest k^(1/k), for any natural number k, occurs when k = 3 = A000227(1). - Stanislav Sykora, Jun 04 2014
3^(1/3) is also the Kolmogorov constant C(3,2) in the case supremum norm on the real line. - Jean-François Alcover, Jul 17 2014
(1/3)*log(3) = -lim_{n->oo} (n-th derivative zeta(n+1)) / ((n-1)-th derivative zeta(n)) = 0.3662040962227... Convergence is to 25 digits by n = ~1000. zeta is the Riemann zeta function. - Richard R. Forberg, Feb 24 2015

			1.442249570307408382321638310780109588391869253499350577546416...

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 cube root of 2, cube root of 3, cube root of 4 and cube root of 9 with chi_2 data, Scripta Math. 18, (1952), 173-176.

Harry J. Smith, Table of n, a(n) for n = 1..20000
Simon Plouffe, The cube root of 3 to 2000 places. [Wayback Machine link]
Simon Plouffe, The cube root of 3 to 2000 places.
Harry Pollard, Problem E 2190, Elementary Problems, The American Mathematical Monthly, Vol. 76, No. 8 (1969), p. 937; A Special Property of 3, Solutions to Problem E 2190, by Douglas Lind and Charles Wexler, ibid., Vol. 77, No. 7 (1970), p. 768.
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. [Annotated scanned copies of pages 175 and 176 only]
Eric Weisstein's MathWorld, Landau-Kolmogorov Constants.
Index entries for algebraic numbers, degree 3.

Cf. A002946 (continued fraction).

RealDigits[N[3^(1/3), 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

default(realprecision, 20080); x=3^(1/3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002581.txt", n, " ", d));  \\ Harry J. Smith, May 07 2009

3^(1/3) >= min(k^(1/m), m^(1/k)) for any positive integers k and m (Pollard, 1969). - Amiram Eldar, Feb 14 2025

A005480 Decimal expansion of cube root of 4.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane; entry revised Apr 23 2006

Let h = 4^(1/3). Then (h+1,0) is the x-intercept of the shortest segment from the x-axis through (1,2) to the y-axis; see A197008. - Clark Kimberling, Oct 10 2011

Let h = 4^(1/3). The relative maximum of xy(x+y)=1 is (-1/sqrt(h), h). - Clark Kimberling, Oct 05 2020

			1.587401051968199474751705639272308260391493327899853...

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), p. 173-176.

Harry J. Smith, Table of n, a(n) for n = 1..20000
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. [Annotated scanned copies of pages 175 and 176 only]
Index entries for algebraic numbers, degree 3

Cf. A002947 (continued fraction). - Harry J. Smith, May 07 2009

Cf. A002580 (cube root of 2).

RealDigits[N[4^(1/3), 200]] (* Vladimir Joseph Stephan Orlovsky, May 27 2010 *)

default(realprecision, 20080); x=4^(1/3); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005480.txt", n, " ", d));  \\ Harry J. Smith, May 07 2009, with a correction made May 19 2009

Equals Product_{k>=0} (1 + (-1)^k/(3*k + 1)). - Amiram Eldar, Jul 25 2020
Equals A002580^2. - Michel Marcus, Jan 08 2022
Equals hypergeom([1/3, 1/6], [2/3], 1). - Peter Bala, Mar 02 2022

A175379 Decimal expansion of Gamma(1/6).

Original entry on oeis.org

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

Offset: 1

R. J. Mathar, Apr 24 2010

A175379 * A073005 * A002161 * A073006 * A203145 = 4*sqrt(Pi^5/3), which is the case n=6 of Product_{i=1..n-1} Gamma(i/n) = sqrt((2*Pi)^(n-1)/n). - Bruno Berselli, Dec 18 2012

The transcendence of this constant is in the mathematical folklore; see Finch (who credits Nesterenko) and Gun-Murty-Rath. - Charles R Greathouse IV, Nov 11 2013

			Equals 5.56631600178023...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Steven Finch, Errata and addenda to Mathematical Constants (2013)
Sanoli Gun, M. Ram Murty, and Purusottam Rath, Transcendence of the log gamma function and some discrete periods, J. Number Theory (2009), doi:10.1016/j.jnt.2009.01.008
R. Vidunas, Expressions for values of the Gamma function, arxiv:math/0403510 [math.CA], 2004.
Wikipedia, Particular values of the Gamma function: General rational arguments
Index entries for transcendental numbers
Index entries to sequences related to the Gamma function

Cf. A073006, A203145.

SetDefaultRealField(RealField(100)); Gamma(1/6); // G. C. Greubel, Mar 10 2018

Maple
```
evalf(GAMMA(1/6)) ;
```

RealDigits[Gamma[1/6], 10, 110][[1]] (* Bruno Berselli, Dec 13 2012 *)

gamma(1/6) \\ Charles R Greathouse IV, Nov 16 2013

Equals 2*Pi/A203145 = A002194 * A073005^2 / (A002161 * A002580) = A019692 / 1.12878703....

A002945 Continued fraction for cube root of 2.

Original entry on oeis.org

1, 3, 1, 5, 1, 1, 4, 1, 1, 8, 1, 14, 1, 10, 2, 1, 4, 12, 2, 3, 2, 1, 3, 4, 1, 1, 2, 14, 3, 12, 1, 15, 3, 1, 4, 534, 1, 1, 5, 1, 1, 121, 1, 2, 2, 4, 10, 3, 2, 2, 41, 1, 1, 1, 3, 7, 2, 2, 9, 4, 1, 3, 7, 6, 1, 1, 2, 2, 9, 3, 1, 1, 69, 4, 4, 5, 12, 1, 1, 5, 15, 1, 4

Offset: 0

N. J. A. Sloane

			2^(1/3) = 1.25992104989487316... = 1 + 1/(3 + 1/(1 + 1/(5 + 1/(1 + ...)))).

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
BCMATH, Continued fraction expansion of the n-th root of a positive rational.
E. Bombieri and A. J. van der Poorten, Continued fractions of algebraic numbers, In: W. Bosma, A. van der Poorten (eds), Computational Algebra and Number Theory. Mathematics and Its Applications, vol. 325.
Ashok Kumar Gupta and Ashok Kumar Mittal, Bifurcating continued fractions, arXiv:math/0002227 [math.GM] (2000).
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.
Eric Weisstein's World of Mathematics, Delian Constant.
G. Xiao, Contfrac
Index entries for continued fractions for constants

Cf. A002946, A002947, A002948, A002949, A002580 (decimal expansion).

Cf. A002351, A002352 (convergents).

ContinuedFraction(2^(1/3)); // Vincenzo Librandi, Oct 08 2017

N:= 100: # to get a(1) to a(N)
a[1] := 1: p[1] := 1: q[1] := 0: p[2] := 1: q[2] := 1:
for n from 2 to N do
  a[n] := floor((-1)^(n+1)*3*p[n]^2/(q[n]*(p[n]^3-2*q[n]^3)) - q[n-1]/q[n]);
  p[n+1] := a[n]*p[n] + p[n-1];
  q[n+1] := a[n]*q[n] + q[n-1];
od:
seq(a[i],i=1..N); # Robert Israel, Jul 30 2014

ContinuedFraction[Power[2, (3)^-1],70] (* Harvey P. Dale, Sep 29 2011 *)

allocatemem(932245000); default(realprecision, 21000); x=contfrac(2^(1/3)); for (n=1, 20000, write("b002945.txt", n-1, " ", x[n])); \\ Harry J. Smith, May 08 2009

From Robert Israel, Jul 30 2014: (Start)
Bombieri/van der Poorten give a complicated formula:
a(n) = floor((-1)^(n+1)*3*p(n)^2/(q(n)*(p(n)^3-2*q(n)^3)) - q(n-1)/q(n)),
p(n+1) = a(n)*p(n) + p(n-1),
q(n+1) = a(n)*q(n) + q(n-1),
with a(1) = 1, p(1) = 1, q(1) = 0, p(2) = 1, q(2) = 1. (End)

BCMATH link from Keith R Matthews (keithmatt(AT)gmail.com), Jun 04 2006

Offset changed by Andrew Howroyd, Jul 04 2024

A118292 Decimal expansion of (Gamma(1/6)Gamma(1/3))/(3sqrt(Pi)).

Original entry on oeis.org

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

Offset: 1

Eric W. Weisstein, Apr 22 2006

General formula: Integral_{x=0..1} (1+x^(3n))/sqrt(1-x^3) dx = G_3 * k_n = G_3*A146751(n)/A146752(n) = A118292*A146751(n)/A146752(n) where G_3 = (Gamma(1/3)^3)/(2^(1/3)*sqrt(3)*Pi) is the number in the present entry. For numerators of k_n see A146752, for denominators of k_n see A146753. - Artur Jasinski

gamma(1/6)*gamma(1/3)/(3*sqrt(Pi)) = gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi). - Harry J. Smith, May 09 2009

			2.8043642106509085223500381581005882709260444108....

Harry J. Smith, Table of n, a(n) for n = 1..4000
Eric Weisstein's World of Mathematics, Butterfly Curve

Cf. A146752, A146753, A160323 (continued fraction).

RealDigits[(Gamma[1/3]^3)/(2^(1/3) Sqrt[3] Pi), 10, 200] (* Artur Jasinski*)

allocatemem(932245000); default(realprecision, 4080); x=gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi); for (n=1, 4000, d=floor(x); x=(x-d)*10; write("b118292.txt", n, " ", d)) \\ Harry J. Smith, Jun 20 2009

3/hypergeom([1/3,1/6],[3/2],1) \\ Charles R Greathouse IV, Aug 29 2025

Equals A073005^3 / (A002194*A002580*A000796) [see Vidunas, arXiv:math.CA/0403510]. - R. J. Mathar, Nov 30 2008

Equals 3/hypergeom([1/3, 1/6], [3/2], 1) = A290570*A005480. - Peter Bala, Mar 02 2022

Edited by N. J. A. Sloane, Nov 16 2008 at the suggestion of R. J. Mathar

A005531 Decimal expansion of fifth root of 2.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

The sine of 2017 times this number is the near-integer 0.999999999999999978567771261.... - Alonso del Arte, May 03 2013

With the present number r = 2^(1/5) and the golden section phi = A001622 the other (complex) roots of x^5 - 2 are given by x1 = r*exp(2*Pi*i/5) = r*(phi - 1 + sqrt(2 + phi)*i)/2 = r*(A001622 - 1 + A188593*i)/2 = 0.3549673131... + 1.0924770557...*i, x2 = r*exp(4*Pi*i/5) = r*(-phi + sqrt(3 - phi)*i)/2 = r*(-A001622 + A182007*i)/2 = -0.9293164906... + 0.6751879523...*i, and their complex conjugates. - Wolfdieter Lang, Dec 06 2022

			1.148698354997035006798626946777927589443850889097797505513711118493603....

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 = 1..20000
Index entries for algebraic numbers, degree 5.

Cf. A002950 (continued fraction).
Cf. A002580 (cube root of 2).
Cf. A001622, A182007, A188593.

RealDigits[N[2^(1/5),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)
RealDigits[Surd[2,5],10,120][[1]] (* Harvey P. Dale, May 08 2025 *)

{ default(realprecision, 20080); x=2^(1/5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b005531.txt", n, " ", d)); } \\ Harry J. Smith, May 12 2009

Equals Product_{k>=0} (1 + (-1)^k/(5*k + 4)). - Amiram Eldar, Jul 25 2020
From Peter Bala, Mar 02 2022: (Start)
Equals (3/2)*Sum_{n >= 0} (1/(5*n+2) - 1/(5*n-3))*binomial(1/5,n). Cf. A002580.
Equals (5/4)*hypergeom([-1/5, -3/5], [7/5], -1). (End)

More terms from Olaf Voß, Feb 13 2008

A010768 Decimal expansion of 6th root of 2.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

			1.12246204...

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Index entries for algebraic numbers, degree 6.

RealDigits[N[2^(1/6), 100]][[1]] (* Vincenzo Librandi, Mar 31 2013 *)

sqrtn(2,6) \\ Charles R Greathouse IV, Apr 15 2014

Equals Product_{k>=0} (1 + (-1)^k/(6*k + 5)). - Amiram Eldar, Jul 25 2020

Equals sqrt(A002580). - R. J. Mathar, Jan 15 2021

cp's OEIS Frontend

A129702 Egyptian Fraction representation for the cube root of 2.

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A010466 Decimal expansion of square root of 8.

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A017979 Powers of cube root of 2 rounded down.

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A002581 Decimal expansion of cube root of 3.

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A005480 Decimal expansion of cube root of 4.

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A175379 Decimal expansion of Gamma(1/6).

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A002945 Continued fraction for cube root of 2.

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A118292 Decimal expansion of (Gamma(1/6)Gamma(1/3))/(3sqrt(Pi)).