A020805 -id:A020805 - cp's OEIS frontend

A010502 Decimal expansion of square root of 48.

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

A249386 Decimal expansion of the constant 'a' appearing in the asymptotic expression of the number of plane partitions of n as an^(-25/36)exp(b*n^(2/3)).

Original entry on oeis.org

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

Offset: 0

Jean-François Alcover, Oct 27 2014

The paper by Finch contains an error: the denominator should be sqrt(3*Pi), not sqrt(Pi). The constant 0.4009988836 is wrong. The formula in A000219 and the article by L. Mutafchiev and E. Kamenov (page 6) is correct. - Vaclav Kotesovec, Oct 27 2014. [In new version of prt.pdf is already corrected. - Vaclav Kotesovec, May 11 2015]

			0.231516813448898370560356406406332110855129212593287926597944524...

G. C. Greubel, Table of n, a(n) for n = 0..5000
Steven Finch, Integer Partitions, September 22, 2004. [Cached copy, with permission of the author]
L. Mutafchiev and E. Kamenov, On The Asymptotic Formula for the Number of Plane Partitions of Positive Integers, arXiv:math/0601253 [math.CO], 2006; C. R. Acad. Bulgare Sci. 59(2006), No. 4, 361-366.

Cf. A000219, A020805, A084448, A239049.

a = Zeta[3]^(7/36)*Exp[Zeta'[-1]]/(2^(11/36)*Sqrt[3*Pi]); RealDigits[a, 10, 104] // First

Equals zeta(3)^(7/36)*exp(zeta'(-1))/(2^(11/36)*sqrt(3*Pi)).

Equals exp(1/12) * A002117^(7/36) / (A074962 * 2^(11/36) * sqrt(3*Pi)). - Vaclav Kotesovec, Mar 02 2015

A321120 Decimal expansion of (3 + sqrt(3))/12.

Original entry on oeis.org

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

Offset: 0

Franck Maminirina Ramaharo, Nov 09 2018

The smallest weight in Holladay-Sard's quadrature formula for semi-infinite integrals.

			0.3943375672974064411272871951...

Harold J. Ahlberg, Edwin N. Nilson and Joseph L. Walsh, The Theory of Splines and Their Applications, Academic Press, 1967.

John C. Holladay, A smoothest curve approximation, Math. Comp. Vol. 11 (1957), 233-243.
Leroy F. Meyers and Arthur Sard, Best approximate integration formulas, J. Math. Phys. Vol. 29 (1950), 118-123.
Arthur Sard, Best approximate integration formulas; best approximation formulas, American Journal of Mathematics Vol. 71 (1949), 80-91.
Frans Schurer, On natural cubic splines, with an application to numerical integration formulae, EUT report. WSK, Dept. of Mathematics and Computing Science Vol. 70-WSK-04 (1970), 1-32.

Cf. A020805, A165663.

Cf. A321118, A321119.

Digits := 1000; evalf((3 + sqrt(3))/12);

RealDigits[(3 + Sqrt[3])/12, 10, 100][[1]]

PARI
```
(3 + sqrt(3))/12
```

Equals lim_{n->infinity} A321118(0,n)/A321119(n).
Irrational number represented by the periodic continued fraction [0, 2, 1, 1; [6, 2]].
Largest real root of 1 - 12*x + 24*x^2.

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A010502 Decimal expansion of square root of 48.

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A249386 Decimal expansion of the constant 'a' appearing in the asymptotic expression of the number of plane partitions of n as an^(-25/36)exp(b*n^(2/3)).

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A321120 Decimal expansion of (3 + sqrt(3))/12.

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cp's OEIS Frontend

A010502 Decimal expansion of square root of 48.

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A249386 Decimal expansion of the constant 'a' appearing in the asymptotic expression of the number of plane partitions of n as a*n^(-25/36)*exp(b*n^(2/3)).

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A321120 Decimal expansion of (3 + sqrt(3))/12.

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Author

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Maple

Mathematica

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Formula

A249386 Decimal expansion of the constant 'a' appearing in the asymptotic expression of the number of plane partitions of n as an^(-25/36)exp(b*n^(2/3)).