A002193 -id:A002193 - cp's OEIS frontend

A113024 Decimal expansion of Sum_{k>=1} -(-1)^k/sqrt(k).

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

Offset: 0

Robert G. Wilson v, Oct 11 2005

			1 - 1/sqrt(2) + 1/sqrt(3) - 1/sqrt(4) + 1/sqrt(5) - 1/sqrt(6) + 1/sqrt(7) ... =
0.60489864342163037024726591423595549975976254513024738037854664808...

Stephen Fletcher Hewson, A Mathematical Bridge: An Intuitive Journey In Higher Mathematics, World Scientific, NJ, 2003, p. 83.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Rick Kreminski, Using Simpson's rule to approximate sums of infinite series, Coll. Math. J. 28 (5) (1997), p 368-376, Table 1.
Eric Weisstein's World of Mathematics, Zeta Function.

Cf. A002193, A059750, A263192, A263193, A265162.

Zeta(0,1/2,1/2); evalf(%) ; # R. J. Mathar, Dec 17 2024

RealDigits[(1 - Sqrt[2])Zeta[1/2], 10, 111][[1]]

(1-sqrt(2))*zeta(1/2) \\ G. C. Greubel, Apr 09 2018

Equals (1-sqrt(2))*zeta(1/2) = (-1+A002193) * A059750.
A265162/A113024 = gamma/2 + Pi/4 - (1/2 + sqrt(2))*log(2) + log(Pi)/2, where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Dec 03 2015
Equals -zeta(1/2, 1/2). - Peter Luschny, Nov 03 2020

A131594 Decimal expansion of sqrt(2)/3, the volume of a regular octahedron with edge length 1.

Original entry on oeis.org

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

Offset: 0

Omar E. Pol, Aug 30 2007

Volume of a regular octahedron: V = ((sqrt(2))/3)* a^3, where 'a' is the edge.

			0.471404520791031682933896...

Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 450.

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Wikipedia, Platonic solid.
Index entries for algebraic numbers, degree 2.

Cf. A020829 (regular tetrahedron volume), A102208 (regular icosahedron volume), A102769 (regular dodecahedron volume).

Cf. A179587.

RealDigits[Sqrt[2]/3,10,120][[1]] (* Harvey P. Dale, May 27 2012 *)

PARI
```
sqrt(2)/3 \\ G. C. Greubel, Jul 06 2017
```

Equals A002193/3 = A010464/A010482. - R. J. Mathar, Dec 11 2009

More digits from R. J. Mathar, Dec 11 2009

A156649 Decimal expansion of (9+4*sqrt(2))/7.

Original entry on oeis.org

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

Offset: 1

Klaus Brockhaus, Feb 13 2009

lim_{n -> infinity} b(n)/b(n-1) = ((9+4*sqrt(2))/7)/((19+6*sqrt(2))/17) for n mod 9 = {1, 2}, b = A129837, A156650.

			(9+4*sqrt(2))/7 = 2.09383632135605431360...

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for algebraic numbers, degree 2

Cf. A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)). A156163 (decimal expansion of (19+6*sqrt(2))/17), A129837, A156650.

RealDigits[(9 + 4*Sqrt[2])/7, 10, 100][[1]] (* G. C. Greubel, Jul 05 2017 *)

(9+4*sqrt(2))/7 \\ G. C. Greubel, Jul 05 2017

A246724 Decimal expansion of r_2, the second smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_2.

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Sep 02 2014

Essentially the same digit sequence as A176053 and A020832. - R. J. Mathar, Sep 06 2014
This equals the ratio of the radius of the inner Soddy circle and the common radius of the three kissing circles. See A343235, also for links. - Wolfdieter Lang, Apr 19 2021
Previous comment is, together with A176053, the answer to the 1st problem proposed during the 4th Canadian Mathematical Olympiad in 1972. - Bernard Schott, Mar 16 2022

			0.154700538379251529018297561003914911295203502540253752...

Michael Doob, The Canadian Mathematical Olympiad & L'Olympiade Mathématique du Canada 1969-1993 - Canadian Mathematical Society & Société Mathématique du Canada, Problem 1, 1972, page 37, 1993.

Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2021, p. 62.
The IMO Compendium, Problem 1, 4th Canadian Mathematical Olympiad, 1972.
Samuel G. Moreno and Esther M. García, New infinite products of cosines and Viète-like formulae, Mathematics Magazine, Vol. 86, No. 1 (2013), pp. 15-25.
Bernard Schott, Soddy circles.
Index entries for algebraic numbers, degree 2.
Index to sequences related to Olympiads.

Cf. A246723 (r_1), A246725 (r_3), A246726 (r_4), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).

Cf. A176053, A343235.

RealDigits[(2*Sqrt[3] - 3)/3, 10, 103] // First

2/sqrt(3) - 1 \\ Charles R Greathouse IV, Feb 10 2025

Equals (2*sqrt(3) - 3)/3.
Equals A176053 - 2.
Equals -1 + sqrt(2) * sqrt(2-sqrt(2)) * sqrt(2-sqrt(2-sqrt(2))) * ... (Moreno and García, 2013). - Amiram Eldar, Jun 09 2022

A068092 Index of smallest triangular number with n digits.

Original entry on oeis.org

1, 4, 14, 45, 141, 447, 1414, 4472, 14142, 44721, 141421, 447214, 1414214, 4472136, 14142136, 44721360, 141421356, 447213595, 1414213562, 4472135955, 14142135624, 44721359550, 141421356237, 447213595500, 1414213562373, 4472135955000, 14142135623731

Offset: 1

Amarnath Murthy, Feb 19 2002

Look at the interleaving of the decimal expansion of the square roots of 2 and 20.

			a(4) = 45 as the 45th triangular number is 45*46/2 = 1035 while the 44th is 990.

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A002024, A002193, A010476.

Cf. A068093, A068094, A095863, A095864, A095865, A095866.

[Round(Sqrt(2*10^(n-1))) : n in [1..30]]; // Vincenzo Librandi, Oct 05 2011

f[n_] := Block[{a = Floor[Sqrt[2*10^n]]}, If[a(a + 1)/2 < 10^n, a++ ]; Return[a]]; Table[ f[n], {n, 0, 30} ]

a(n) = round(sqrt(2*10^(n-1))) \\ Charles R Greathouse IV, Oct 04 2011

from math import isqrt
def A068092(n): return isqrt(10**(n-1)<<3)+1>>1 # Chai Wah Wu, Oct 17 2022

a(n) = b where b = floor(sqrt(2*10^(n-1))) and if b(b+1)/2 < 10^(n-1), then b = b+1. [corrected by Ray Chandler, Oct 04 2011]
a(n) = round((2*10^(n-1))^(1/2)). - Vladeta Jovovic, Mar 08 2004
a(n) = A002024(10^(n-1)). - Michel Marcus, Jan 27 2022

Edited and extended by Robert G. Wilson v, Feb 21 2002

A092678 Decimal expansion of the probable error.

Original entry on oeis.org

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

Offset: 0

Eric W. Weisstein, Mar 03 2004

0.75 percentile of the normal probability distribution function. In a bilateral sense, normally distributed random values x are equally likely to fall inside the interval (-a*sigma, +a*sigma) as to fall outside, "a" being this constant. - Stanislav Sykora, Nov 08 2013

			InverseErf(1/2) * sqrt(2) = 0.674489750...

Stanislav Sykora, Table of n, a(n) for n = 0..9999
Stanislav Sykora, PARI/GP scripts for NormalErrorFunctions.
Eric Weisstein's World of Mathematics, Standard Normal Distribution
Eric Weisstein's World of Mathematics, Probable Error

Cf. A002193, A069286.

RealDigits[ Sqrt[2] InverseErf[1/2], 10, 111][[1]] (* Robert G. Wilson v, Feb 11 2015 *)

PARI
```
See the links.
```

solve(x=0,1,erfc(x)-1/2)*sqrt(2) \\ Charles R Greathouse IV, Oct 15 2015

Equals A069286 * A002193.

A103710 Decimal expansion of the ratio of the length of the latus rectum arc of any parabola to its semi latus rectum: sqrt(2) + log(1 + sqrt(2)).

Original entry on oeis.org

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

Offset: 1

Sylvester Reese and Jonathan Sondow, Feb 13 2005

The universal parabolic constant, equal to the ratio of the latus rectum arc of any parabola to its focal parameter. Like Pi, it is transcendental.
Just as all circles are similar, all parabolas are similar. Just as the ratio of a semicircle to its radius is always Pi, the ratio of the latus rectum arc of any parabola to its semi latus rectum is sqrt(2) + log(1 + sqrt(2)).
Note the remarkable similarity to sqrt(2) - log(1 + sqrt(2)), the universal equilateral hyperbolic constant A222362, which is a ratio of areas rather than of arc lengths. Lockhart (2012) says "the arc length integral for the parabola .. is intimately connected to the hyperbolic area integral ... I think it is surprising and wonderful that the length of one conic section is related to the area of another."
Is it a coincidence that the universal parabolic constant is equal to 6 times the expected distance A103712 from a randomly selected point in the unit square to its center? (Reese, 2004; Finch, 2012)

			2.29558714939263807403429804918949038759783220363858348392997534664...

H. Dörrie, 100 Great Problems of Elementary Mathematics, Dover, 1965, Problems 57 and 58.
P. Lockhart, Measurement, Harvard University Press, 2012, p. 369.
C. E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, pp. 286-288.
C. S. Ogilvy, Excursions in Geometry, Oxford Univ. Press, 1969, p. 84.
S. Reese, A universal parabolic constant, 2004, preprint.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
J. L. Diaz-Barrero and W. Seaman, A limit computed by integration, Problem 810 and Solution, College Math. J., 37 (2006), 316-318, equation (5).
S. R. Finch, Mathematical Constants, Errata and Addenda, 2012, section 8.1.
M. Hajja, Review Zbl 1291.51018, zbMATH 2015.
M. Hajja, Review Zbl 1291.51016, zbMATH 2015.
H. Khelif, L’arbelos, Partie II, Généralisations de l’arbelos, Images des Mathématiques, CNRS, 2014.
J. Pahikkala, Arc Length Of Parabola, PlanetMath.
S. Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, Feb 02 2005
S. Reese, Jonathan Sondow, Eric W. Weisstein, MathWorld: Universal Parabolic Constant
Manas Shetty, Prajwal DSouza, Sparsha Kumari, Vinton Adrian Rebello, Where is the Parabola? The Parabolic Constant Mystery
Jonathan Sondow, The parbelos, a parabolic analog of the arbelos, arXiv 2012, Amer. Math. Monthly, 120 (2013), 929-935.
E. Tsukerman, Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos, arXiv 2012, Amer. Math. Monthly, 121 (2014), 438-443.
Wikipedia, Universal parabolic constant
Index entries for transcendental numbers

A002193 + A091648.

Cf. A103711, A103712, A222362, A232716, A232717.

RealDigits[ Sqrt[2] + Log[1 + Sqrt[2]], 10, 111][[1]] (* Robert G. Wilson v Feb 14 2005 *)

fpprec: 100$ ev(bfloat(sqrt(2) + log(1 + sqrt(2)))); /* Martin Ettl, Oct 17 2012 */

sqrt(2)+log(1+sqrt(2)) \\ Charles R Greathouse IV, Mar 08 2013

Equals 2*Integral_{x = 0..1} sqrt(1 + x^2) dx. - Peter Bala, Feb 28 2019

A240572 a(n) = floor(4^n/(2 + sqrt(2))^n).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 9, 10, 12, 14, 17, 20, 23, 27, 32, 38, 44, 52, 61, 71, 84, 98, 115, 135, 158, 185, 217, 255, 299, 350, 410, 480, 563, 659, 773, 905, 1061, 1243, 1456, 1706, 1999, 2342, 2744, 3215, 3767, 4413, 5170, 6057, 7097, 8314

Offset: 0

Kival Ngaokrajang, Apr 08 2014

a(n) is the perimeter (rounded down) of octaflake after n iterations, let a(0) = 1. The total number of sides is 8*A000302(n). The total number of holes is A084990(A000225(n)). sqrt(2) = A002193.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration of octaflake for n = 0..3
Wikipedia, n-flake

Cf. A000302, A084990, A000225, A002193. A240523 (pentaflake), A240671 (heptaflake), A240733 (nonaflake), A240734 (decaflake), A230735 (dodecaflake).

A240572:=n->floor(4^n/(2 + sqrt(2))^n); seq(A240572(n), n=0..50); # Wesley Ivan Hurt, Apr 12 2014

Table[Floor[4^n/(2 + Sqrt[2])^n], {n, 0, 50}] (* Wesley Ivan Hurt, Apr 12 2014 *)

{a(n)=floor(4^n/(2 + sqrt(2))^n)}
       for (n=0, 100, print1(a(n), ", "))

A103712 Decimal expansion of the expected distance from a randomly selected point in the unit square to its center: (sqrt(2) + log(1 + sqrt(2)))/6.

Original entry on oeis.org

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

Offset: 0

Sylvester Reese and Jonathan Sondow, Feb 13 2005

Is it a coincidence that this constant is equal to 1/6 of the universal parabolic constant A103710? (Reese, 2004; Finch, 2012)
exp(d(2)) - exp(d(2))/Pi = 0.9994179247351742... ~ 1 - 1/1718. - Gerald McGarvey, Feb 21 2005
Take a point on a line of irrational slope and a line segment of a given length centered at the point, integrate the distance of a point on the line to the set of lattice points along the line segment, and divide by the length. The limit as the length approaches infinity can be shown by a generalization of the Equidistribution Theorem to give the expected distance of a point in the unit square to its corners, this constant. - Thomas Anton, Jun 19 2021

			0.38259785823210634567238300819824839793297203393976391398832922444...

Steven R. Finch, Mathematical Constants, Cambridge, 2003, section 8.1.
S. Reese, A universal parabolic constant, 2004, preprint.

Ivan Panchenko, Table of n, a(n) for n = 0..1000
Steven R. Finch, Mathematical Constants, Errata and Addenda, 2012, section 8.1.
Sylvester Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, February 2005.
Sylvester Reese, Jonathan Sondow and Eric W. Weisstein, MathWorld: Universal Parabolic Constant.
Eric Weisstein's World of Mathematics, Universal Parabolic Constant.
Eric Weisstein's World of Mathematics, Square Line Picking.
Wikipedia, Universal parabolic constant.
Index entries for transcendental numbers.

Equal to (A002193 + A091648)/6 = (A103710)/6 = (A103711)/3.

Cf. A244921.

RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/6, 10, 111][[1]] (* Robert G. Wilson v, Feb 14 2005 *)

fpprec: 100$ ev(bfloat((sqrt(2) + log(1 + sqrt(2)))/6)); /* Martin Ettl, Oct 17 2012 */

(sqrt(2) + log(1 + sqrt(2)))/6 \\ G. C. Greubel, Sep 22 2017

Equals (1/3)*Integral_{x = 0..1} sqrt(1 + x^2) dx. - Peter Bala, Feb 28 2019
Equals Integral_{x>=1} arcsinh(x)/x^4 dx. - Amiram Eldar, Jun 26 2021
Equals A244921 / 2. - Amiram Eldar, Jun 04 2023

A135611 Decimal expansion of sqrt(2) + sqrt(3).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Mar 03 2008

From Alexander R. Povolotsky, Mar 04 2008: (Start)
The value of sqrt(2) + sqrt(3) ~= 3.146264369941972342329135... is "close" to Pi. [See Borel 1926. - Charles R Greathouse IV, Apr 26 2014] We can get a better approximation by solving the equation: (2-x)^(1/(2+x)) + (3-x)^(1/(2+x)) = Pi.
Olivier Gérard finds that x is 0.00343476569746030039595770020414255107204742044644777... (End)
Another approximation to Pi is (203*sqrt(2)+ 197*sqrt(3))/200 = 3.1414968... - Alexander R. Povolotsky, Mar 22 2008
Shape of a sqrt(8)-extension rectangle; see A188640.  - Clark Kimberling, Apr 13 2011
This number is irrational, as instinct would indicate. Niven (1961) gives a proof of irrationality that requires first proving that sqrt(6) is irrational. - Alonso del Arte, Dec 07 2012
An algebraic integer of degree 4: largest root of x^4 - 10*x^2 + 1. - Charles R Greathouse IV, Sep 13 2013
Karl Popper considers whether this approximation to Pi might have been known to Plato, or even conjectured to be exact. - Charles R Greathouse IV, Apr 26 2014

			3.14626436994197234232913506571557044551247712918732870...

Emile Borel, Space and Time (1926).
Ivan Niven, Numbers: Rational and Irrational. New York: Random House for Yale University (1961): 44.
Ian Stewart & David Tall, Algebraic Number Theory and Fermat's Last Theorem, 3rd Ed. Natick, Massachusetts: A. K. Peters (2002): 44.

G. C. Greubel, Table of n, a(n) for n = 1..2500
Susan Landau, Simplification of nested radicals, SIAM Journal on Computing 21.1 (1992): 85-110. See page 85. [Do not confuse this paper with the short FOCS conference paper with the same title, which is only a few pages long.]
Burkard Polster, Irrational roots, Mathologer video (2018)
Karl Popper, The Open Society and Its Enemies, 1962.
Index entries for algebraic numbers, degree 4

Cf. A188640, A089078, A002193, A002194, A010464, A340616.

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

evalf(add(sqrt(ithprime(i)), i=1..2), 118);  # Alois P. Heinz, Jun 13 2022

r = 8^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (* A135611 *)
ContinuedFraction[t, 120]  (* A089078 *)
RealDigits[Sqrt[2] + Sqrt[3], 10, 100][[1]] (* G. C. Greubel, Oct 22 2016 *)

sqrt(2)+sqrt(3) \\ Charles R Greathouse IV, Sep 13 2013

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

Sqrt(2)+sqrt(3) = sqrt(5+2*sqrt(6)). [Landau, p. 85] - N. J. A. Sloane, Aug 27 2018
Equals 1/A340616. - Hugo Pfoertner, May 08 2024
Equals Product_{k>=0} (((4*k + 1)*(12*k + 11))/((4*k + 3)*(12*k + 1)))^(-1)^k. - Antonio Graciá Llorente, May 22 2024

cp's OEIS Frontend

A113024 Decimal expansion of Sum_{k>=1} -(-1)^k/sqrt(k).

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A131594 Decimal expansion of sqrt(2)/3, the volume of a regular octahedron with edge length 1.

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A156649 Decimal expansion of (9+4*sqrt(2))/7.

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A246724 Decimal expansion of r_2, the second smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_2.

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A068092 Index of smallest triangular number with n digits.

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A092678 Decimal expansion of the probable error.

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