A002194 -id:A002194 - cp's OEIS frontend

A010469 Decimal expansion of square root of 12.

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

Offset: 1

N. J. A. Sloane

3+sqrt(12) is the ratio of the radii of the three identical kissing circles to that of their inner Soddy circle. - Lekraj Beedassy, Mar 04 2006
sqrt(12)-3 = 2*sqrt(3)-3 is the area of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link). - Rick L. Shepherd, Jun 24 2006
Continued fraction expansion is 3 followed by {2, 6} repeated (A040008). - Harry J. Smith, Jun 02 2009
Surface of a regular octahedron with unit edge, and twice the surface of a regular tetrahedron with unit edge. - Stanislav Sykora, Nov 21 2013
Imaginary part of the square of a complex cubic root of 64 (real part is -2). - Alonso del Arte, Jan 13 2014

			3.4641016151377545870548926830...

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 2.31.4 and 2.31.5, pp. 201-202.
Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 450.

Harry J. Smith, Table of n, a(n) for n = 1..20000
Eric Weisstein's World of Mathematics, Equilateral Triangle.
Wikipedia, Octahedron.
Wikipedia, Platonic solid.
Index entries for algebraic numbers, degree 2.

Cf. A120683.
Cf. A040008 (continued fraction), A041016 (numerators of convergents), A041017 (denominators).
Cf. A002194 (surface of tetrahedron), A010527 (surface of icosahedron/10), A131595 (surface of dodecahedron).

evalf[100](sqrt(12)); # Muniru A Asiru, Feb 12 2019

RealDigits[N[Sqrt[12], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)

default(realprecision, 20080); x=sqrt(12); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010469.txt", n, " ", d));  \\ Harry J. Smith, Jun 02 2009

Equals 2*sqrt(3) = 2*A002194. - Rick L. Shepherd, Jun 24 2006

A118325 (Greedy) Egyptian fraction expansion of frac(sqrt(3)) = sqrt(3)-1.

Original entry on oeis.org

2, 5, 32, 1249, 5986000, 438522193400489, 3126430743599145840898147625516, 10008815260914521335142941393259537613217919681721512170785592

Offset: 1

Eric W. Weisstein, Apr 23 2006

			sqrt(3) - 1 = 1/2 + 1/5 + 1/32 + 1/1249 + 1/5986000 + ...

Amiram Eldar, Table of n, a(n) for n = 1..12
Eric Weisstein's World of Mathematics, Egyptian Fraction.
Index entries for sequences related to Egyptian fractions.

Cf. A002194. See A224231 for another version.

lst={};k=N[(Sqrt[3]-1),1000];Do[s=Ceiling[1/k];AppendTo[lst,s];k=k-1/s,{n,12}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 02 2009 *)

A090388 Decimal expansion of 1 + sqrt(3).

Original entry on oeis.org

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

Offset: 1

Felix Tubiana, Feb 05 2004

1 + sqrt(3) is the length of the minimal Steiner network that connects the four vertices of a unit square. - Lekraj Beedassy, May 02 2008
This is the case n = 12 in the identity (Gamma(1/n)/Gamma(3/n))*(Gamma((n-1)/n)/Gamma((n-3)/n)) = 1 + 2*cos(2*Pi/n). - Bruno Berselli, Dec 14 2012
Equals n + n/(n + n/(n + n/(n + ...))) for n = 2. - Stanislav Sykora, Jan 23 2014
A non-optimal solution to the problem of finding the length of shortest fence that protects privacy of a square garden [Kawohl]. Cf. A256965. - N. J. A. Sloane, Apr 14 2015
Perimeter of a 30-60-90 triangle with longest leg equal to 1. - Wesley Ivan Hurt, Apr 09 2016
Length of the second shortest diagonal in a regular 12-gon with unit side. - Mohammed Yaseen, Dec 13 2020
Surface area of a square pyramid (Johnson solid J_1) with unit edges. - Paolo Xausa, Aug 04 2025

			2.7320508075688772...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Bernd Kawohl, Some nonconvex shape optimization problems, in: Optimal Shape Design, Eds. A.Cellina u. A. Ornelas, Springer Lecture Notes in Math.1740 (2000), p. 7-46.
Ian Stewart, Pursuing Polygonal Privacy, Mathematical Recreations Column, Scientific American, 284 (No. 2, 2001), 88-89.
Wikipedia, Square pyramid.
Index entries for algebraic numbers, degree 2

Cf. n + n/(n + n/(n + ...)): A090458 (n = 3), A090488 (n = 4), A090550 (n = 5), A092294 (n = 6), A092290 (n = 7), A090654 (n = 8), A090655 (n = 9), A090656 (n = 10). - Stanislav Sykora, Jan 23 2014

Cf., also A256965.

Digits:=100: evalf((1+sqrt(3))); # Wesley Ivan Hurt, Apr 09 2016

RealDigits[1 + Sqrt[3], 10, 100][[1]] (* Alonso del Arte, Feb 23 2014 *)

1 + sqrt(3) \\ Michel Marcus, Apr 10 2016

Equals 1 + A002194. - R. J. Mathar, Oct 16 2015

Equals A019973 -1 . - R. J. Mathar, May 25 2023

Better definition from Rick L. Shepherd, Jul 02 2004

A248897 Decimal expansion of Sum_{i >= 0} (i!)^2/(2*i+1)!.

Original entry on oeis.org

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

Offset: 1

Bruno Berselli, Mar 06 2015

Value of the Borwein-Borwein function I_3(a,b) for a = b = 1. - Stanislav Sykora, Apr 16 2015

The area of a circle circumscribing a unit-area regular hexagon. - Amiram Eldar, Nov 05 2020

			1.2091995761561452337293855050947704881893774987284937170465899569254...

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), pp. 120-121.
L. B. W. Jolley, Summation of Series, Dover (1961), No. 261, pp. 48, 49, (and No. 275).

Xavier Gourdon and Pascal Sebah, Collection of series for Pi (see paragraph 7).
Su Hu and Min-Soo Kim, A generalization of Wallis' formula, arXiv:2201.09674 [math.NT], 2022.
Richard Kershner, The Number of Circles Covering a Set, American Journal of Mathematics, 61(3), 665-671.
MIT Integration Bee, 2023 MIT Integration Bee - Finals, Problem 1.
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), C6.2.
Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27
László Fejes Tóth, An Inequality concerning polyhedra, Bull. Amer. Math. Soc. 54 (1948), 139-146. See (9) p. 146.
Eric Weisstein's World of Mathematics, Arithmetic-Geometric Mean, equations 26-32.
Index entries for transcendental numbers

Cf. A000796, A001651, A002194, A093602, A248181, A257096, A257097, A186706.
Cf. A010815, A073010, A086089, A214549, A256923, A275486.
Cf. A091682 (Sum_{i >= 0} (i!)^2/(2*i)!).

RealDigits[2 Sqrt[3] Pi/9, 10, 100][[1]]

a = 2*Pi/(3*sqrt(3)) \\ Stanislav Sykora, Apr 16 2015

Equals 2*sqrt(3)*Pi/9 = 1 + 1/6 + 1/30 + 1/140 + 1/630 + 1/2772 + 1/12012 + ...
Equals m*I_3(m,m) = m*Integral_{x>=0} (x/(m^3+x^3)), for any m>0. - Stanislav Sykora, Apr 16 2015
Equals Integral_{x>=0} (1/(1+x^3)) dx. - Robert FERREOL, Dec 23 2016
From Peter Bala, Oct 27 2019: (Start)
Equals 3/4*Sum_{n >= 0} (n+1)!*(n+2)!/(2*n+3)!.
Equals Sum_{n >= 1} 3^(n-1)/(n*binomial(2*n,n)).
Equals 2*Sum_{n >= 1} 1/(n*binomial(2*n,n)). See Boros and Moll, pp. 120-121.
Equals Integral_{x = 0..1} 1/(1 - x^3)^(1/3) dx = Sum_{n >= 0} (-1)^n*binomial(-1/3,n) /(3*n + 1).
Equals 2*Sum_{n >= 1} 1/((3*n-1)*(3*n-2)) = 2*(1 - 1/2 + 1/4 - 1/5 + 1/7 - 1/8 + ...) (added Oct 30 2019). (End)
Equals Product_{k>=1} 9*k^2/(9*k^2 - 1). - Amiram Eldar, Aug 04 2020
From Peter Bala, Dec 13 2021: (Start)
Equals (2/3)*A093602.
Conjecture: for k >= 0, 2*sqrt(3)*Pi/9 = (3/2)^k * k!*Sum_{n = -oo..oo} (-1)^n/ Product_{j = 0..k} (3*n + 3*j + 1). (End)
Equals (3/4)*S - 1, where S = A248682. - Peter Luschny, Jul 22 2022
Equals Integral_{x=0..Pi/2} tan(x)^(1/3)/(sin(2*x) + 1) dx. See MIT Link. - Joost de Winter, Aug 26 2023
Continued fraction: 1/(1 - 1/(7 - 12/(12 - 30/(17 - ... - 2*n*(2*n - 1)/((5*n + 2) - ... ))))). See A000407. - Peter Bala, Feb 20 2024
Equals Sum_{n>=2} 1/binomial(n, floor(n/2)); and trivially if "floor" is replaced by "ceiling". - Richard R. Forberg, Aug 30 2024
Equals Product_{k>=2} (1 + (-1)^k/A001651(k)). - Amiram Eldar, Nov 22 2024
Equals 2*A073010 = 1/A086089 = sqrt(A214549) = exp(A256923) = A275486/2. - Hugo Pfoertner, Nov 22 2024
Equals 1 - (1/6) * Sum_{n>=1} A010815(n)/n. - Friedjof Tellkamp, Apr 05 2025
Equals A248181 - 2. - Pontus von Brömssen, Apr 05 2025

A381684 Decimal expansion of the isoperimetric quotient of a truncated tetrahedron.

Original entry on oeis.org

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

Offset: 0

Paolo Xausa, Mar 04 2025

Polya (1954) defines the isoperimetric quotient of a solid as 36*Pi*V^2/S^3, where V and S are the volume and surface area of the solid, respectively.

The isoperimetric quotient of a sphere is 1.

			0.4662292826432950646084875599089894958106273300491...

George Polya, Mathematics and Plausible Reasoning, Vol. 1: Induction and Analogy in Mathematics, Princeton University Press, Princeton, New Jersey, 1954. See pp. 188-189, exercise 43.

Paolo Xausa, Table of n, a(n) for n = 0..10000
P. K. Aravind, How Spherical Are the Archimedean Solids and Their Duals?, The College Mathematics Journal, Vol. 42, Issue 2, 2011, pp. 98-107.
Index entries for transcendental numbers.

Cf. A377274 (surface area), A377275 (volume).

Cf. A000796, A002194.

First[RealDigits[529*Pi/(2058*Sqrt[3]), 10, 100]]

529*Pi/2058/sqrt(3) \\ Charles R Greathouse IV, Aug 19 2025

Equals 36*Pi*A377275^2/(A377274^3).

Equals 529*Pi/(2058*sqrt(3)) = 529*A000796/(2058*A002194).

A010482 Decimal expansion of square root of 27.

Original entry on oeis.org

5, 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

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 5 followed by {5, 10} repeated (A040021). - Harry J. Smith, Jun 04 2009
6 + sqrt(27) represents the surface of a dodecahedron of side equal to one. S = 3*a^2(2 + sqrt(3)) with a = 1. - Vincenzo Librandi, Jul 10 2010
sqrt(27) is the perimeter of an equilateral triangle whose incircle's diameter is 1. - Martin Janecke, May 31 2016
If r = 2*a * sin(3t)/sin(2t) and x*(x^2+y^2) = a * (3x^2-y^2) are respectively a polar equation and a Cartesian equation of the Maclaurin trisectrix, then sqrt(27) * a^2 = area of the loop of this trisectrix = area between the curve and its asymptote (see Mathcurve link). - Bernard Schott, Jul 14 2020
Area of a regular hexagon with side length sqrt(2). - Christoph B. Kassir, Sep 29 2022
The solution of x^sqrt(3)=sqrt(3)^x, see e.g. A360148. - R. J. Mathar, Mar 24 2023
Surface area of a snub disphenoid (Johnson solid J_84) with unit edges. - Paolo Xausa, Aug 02 2025

			5.196152422706631880582339024517617100828415761431141884167420938355799....

Harry J. Smith, Table of n, a(n) for n = 1..20000
Robert Ferréol, MacLaurin trisectrix, Mathcurve.
Wikipedia, Snub disphenoid.
Index to sequences related to curves.
Index entries for algebraic numbers, degree 2

Cf. A040021 (continued fraction), A248254 (Egyptian fraction).

Cf. A104956 (half), A002194 (sqrt(3)).

RealDigits[N[Sqrt[27], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)

default(realprecision, 20080); x=sqrt(27); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010482.txt", n, " ", d));  \\ Harry J. Smith, Jun 04 2009

Equals 3*sqrt(3) = 3 * A002194. - Bernard Schott, Jul 14 2020

Equals 2 * A104956. - Christoph B. Kassir, Oct 02 2022

A019973 Decimal expansion of tangent of 75 degrees.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

An equivalent definition of this sequence: decimal expansion of x > 1 satisfying x^2 - 4*x + 1 = 0. - Arkadiusz Wesolowski, Nov 28 2011
An algebraic integer of degree 2 with minimal polynomial x^2 - 4*x + 1. - Charles R Greathouse IV, Oct 17 2016
Length of the second longest diagonal in a regular 12-gon with unit side. - Mohammed Yaseen, Dec 13 2020

			3.732050807568877293527446341505872366942805253810380628...

G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Ivan Panchenko)
Wikipedia, Exact trigonometric constants.
Index entries for algebraic numbers, degree 2.

Cf. A002194, A019824, A019884, A019913.

Cf. A001075, A001353, A001835, A049310.

SetDefaultRealField(RealField(100)); 2 + Sqrt(3); // G. C. Greubel, Nov 20 2018

RealDigits[Tan[75 Degree],10,120][[1]] (* Harvey P. Dale, Nov 08 2011 *)
RealDigits[2+Sqrt[3], 10, 100][[1]] (* G. C. Greubel, Nov 20 2018 *)

sqrt(3)+2 \\ Charles R Greathouse IV, Oct 17 2016

numerical_approx(2+sqrt(3), digits=100) # G. C. Greubel, Nov 20 2018

Equals 2 + sqrt(3) = 2+A002194 = cotangent of 15 degrees. - Rick L. Shepherd, Jul 04 2004
Equals exp(arccosh(2)). - Amiram Eldar, Aug 07 2023
c^n = A001835(n) + (1 + sqrt(3)) * A001353(n) = A001075(n) + sqrt(3) * A001353(n); where c = 2 + sqrt(3). - Gary W. Adamson, Oct 14 2023
Equals lim_{n->oo} S(n, 4)/ S(n-1, 4), with the S-Chebyshev polynomial (see A049310) S(n, 4) = A001353(n+1). See the A001353 formula from Oct 06 2002 by Gregory V. Richardson. - Wolfdieter Lang, Nov 15 2023
Equals A019884 / A019824. - R. J. Mathar, Jan 12 2024
Equals 1/A019913. - Hugo Pfoertner, Mar 24 2024

Checked by Neven Juric (neven.juric(AT)apis-it.hr), Feb 04 2008

A010502 Decimal expansion of square root of 48.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane

sqrt(48)/10 is the area enclosed by Koch's fractal snowflake based on unit-sided equilateral triangle (actually 8/5 times the latter's area). - Lekraj Beedassy, Jan 06 2005
7+sqrt(48) is the ratio of outer to inner Soddy circles' radii for three identical kissing circles (see Soddy circles link). - Lekraj Beedassy, Feb 14 2006
Continued fraction expansion is 6 followed by {1, 12} repeated. - Harry J. Smith, Jun 06 2009
Let a, b, c the sides of a triangle ABC of area S, then 4*sqrt(3) <= (a^2+b^2+c^2) / S; equality is obtained only when the triangle is equilateral (see Mitrinovic reference). - Bernard Schott, Sep 27 2022
Surface area of a gyroelongated square bipyramid (Johnson solid J_17) with unit edges. - Paolo Xausa, Aug 02 2025

			6.928203230275509174109785366023489467771221015241522512223227917807732...

J. N. Kapur, Mathematics Enjoyment For The Millions, Problem 47 pp. 64-67, Arya Book Depot, New Delhi 2000.
D. S. Mitrinovic, E. S. Barnes, D. C. B. Marsh, J. R. M. Radok, Elementary Inequalities, Tutorial Text 1 (1964), P. Noordhoff LTD, Groningen, problem 6.3, page 112.

Harry J. Smith, Table of n, a(n) for n = 1..20000
L. Riddle, Area of the Koch Snowflake
Bernard Schott, Soddy circles
Wikipedia, Gyroelongated square bipyramid.
Index entries for algebraic numbers, degree 2

Cf. A040041 (continued fraction).

Cf. A002194, A104956, A010527, A152623 (other geometric inequalities).

RealDigits[N[Sqrt[48],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2011 *)

default(realprecision, 20080); x=sqrt(48); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010502.txt", n, " ", d));  \\ Harry J. Smith, Jun 06 2009

Equals 4*A002194. - R. J. Mathar, Jul 31 2010
Equals A176053/A246724 - 7 (2nd comment and Soddy link). - Bernard Schott, Mar 17 2022
Equals 1/A020805. - Bernard Schott, Sep 28 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....

A019887 Decimal expansion of sine of 78 degrees.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Equals sin(13*Pi/30). - Wesley Ivan Hurt, Aug 31 2014

A quartic number with denominator 2 and minimal polynomial 16x^4 + 8x^3 - 16x^2 - 8x + 1. - Charles R Greathouse IV, Aug 27 2017

			0.9781476007338056379285667478695995324597378088626771078851...

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Exact trigonometric constants
Index entries for algebraic numbers, degree 4

Digits:=100: evalf(sin(13*Pi/30)); # Wesley Ivan Hurt, Aug 31 2014

First@RealDigits[Sin[78 Degree], 10, 120] (* Michael De Vlieger, Aug 31 2014 *)

cos(Pi/15) \\ Charles R Greathouse IV, Aug 27 2017

Equals cos(Pi/15) = [sqrt(5)-1]*[1+sqrt(3)*sqrt{5+2*sqrt(5)}]/8 = [A002163-1]*[1+A002194*A019970]/8. - R. J. Mathar, Jun 18 2006
Equals 2*A019848*A019860. - R. J. Mathar, Jan 17 2021
4*this^3 -3*this = A019863. - R. J. Mathar, Aug 29 2025
Equals 2F1(-1/10,1/10 ; 1/2 ; 3/4). - R. J. Mathar, Aug 31 2025
A root of 16*x^4+8*x^3-16*x^2-8*x+1=0. - R. J. Mathar, Aug 31 2025

cp's OEIS Frontend

A010469 Decimal expansion of square root of 12.

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A118325 (Greedy) Egyptian fraction expansion of frac(sqrt(3)) = sqrt(3)-1.

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A090388 Decimal expansion of 1 + sqrt(3).

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A248897 Decimal expansion of Sum_{i >= 0} (i!)^2/(2*i+1)!.

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A381684 Decimal expansion of the isoperimetric quotient of a truncated tetrahedron.

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A010482 Decimal expansion of square root of 27.

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A019973 Decimal expansion of tangent of 75 degrees.

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