|
| |
|
|
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.
|
|
7
|
|
|
|
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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
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
|
|
|
REFERENCES
|
S. R. Finch, Mathematical Constants, Cambridge, 2003, section 8.1.
S. Reese, A universal parabolic constant, 2004, preprint.
|
|
|
LINKS
|
Ivan Panchenko, Table of n, a(n) for n = 0..1000
S. R. Finch, Mathematical Constants, Errata and Addenda, 2012, section 8.1.
S. Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, Feb 02 2005
S. Reese, J. Sondow, 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
|
|
|
FORMULA
|
Equals 1/3*Integral_{x = 0..1} sqrt(1 + x^2) dx. - Peter Bala, Feb 28 2019
|
|
|
EXAMPLE
|
0.38259785823210634567238300819824839793297203393976391398832922444...
|
|
|
MATHEMATICA
|
RealDigits[(Sqrt[2] + Log[1 + Sqrt[2]])/2, 10, 111][[1]] (* Robert G. Wilson v, Feb 14 2005 *)
|
|
|
PROG
|
(Maxima) fpprec: 100$ ev(bfloat((sqrt(2) + log(1 + sqrt(2)))/6)); /* Martin Ettl, Oct 17 2012 */
(PARI) (sqrt(2) + log(1 + sqrt(2)))/6 \\ G. C. Greubel, Sep 22 2017
|
|
|
CROSSREFS
|
Equal to (A002193 + A091648)/6 = (A103710)/6 = (A103711)/3.
Sequence in context: A202537 A220516 A010627 * A327951 A132019 A182168
Adjacent sequences: A103709 A103710 A103711 * A103713 A103714 A103715
|
|
|
KEYWORD
|
cons,easy,nonn
|
|
|
AUTHOR
|
Sylvester Reese and Jonathan Sondow, Feb 13 2005
|
|
|
STATUS
|
approved
|
| |
|
|
