OFFSET
0,1
COMMENTS
This also equals the probability, for a random walk on the slit plane starting at (1,0), of stopping at the origin.
This is the least real number m such that m*(sqrt(ab) + sqrt(bc) + sqrt(ca)) + sqrt(a^2+b^2+c^2) >= a+b+c where a,b,c are positive real numbers with ab+bc+ca > 0. See the Mathematical Reflections link.
The asymptotical ratio of odd to even powerful numbers (Srichan, 2020). - Amiram Eldar, Mar 07 2021
The volume of the solid formed by the intersection of 3 right circular unit-diameter cylinders whose axes are mutually orthogonal and intersect at a single point (Moore, 1974). - Amiram Eldar, Nov 22 2021
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Mireille Bousquet-Mélou and Gilles Schaeffer, Walks on the slit plane, Probability Theory and Related Fields, Vol. 124, No. 3 (2002), pp. 305-344; arXiv preprint, arXiv:0012230 [math.CO], 2000.
Mathematical Reflections, Solution to Problem J307, Issue 5, 2014, p. 21.
Moreton Moore, Symmetrical Intersections of Right Circular Cylinders, The Mathematical Gazette, Vol. 58, No. 405 (1974), pp. 181-185.
Teerapat Srichan, The Odd/Even Dichotomy For The Set Of Square-Full Numbers, Applied Mathematics E-Notes, Vol. 20 (2020), pp. 528-531.
Eric Weisstein's World of Mathematics, Octagon.
EXAMPLE
0.585786437626904951198311275790301921430328124623051926823320262...
MATHEMATICA
RealDigits[2 - Sqrt[2], 10, 100][[1]] (* G. C. Greubel, Oct 01 2018 *)
PROG
(PARI) 2 - sqrt(2) \\ Michel Marcus, Jan 07 2017
(Magma) SetDefaultRealField(RealField(100)); 2 - Sqrt(2); // G. C. Greubel, Oct 01 2018
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 20 2005
STATUS
approved