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Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.
8

%I #37 Sep 08 2022 08:45:16

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

%T 2,1,4,3,0,3,2,8,1,2,4,6,2,3,0,5,1,9,2,6,8,2,3,3,2,0,2,6,2,0,0,9,2,6,

%U 7,5,2,1,5,3,7,8,9,2,9,6,1,1,4,9,6,1,2,4,6,5,6,7,2,3,5,8,4,2,7,2,6,4,9,8,6

%N Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.

%C This also equals the probability, for a random walk on the slit plane starting at (1,0), of stopping at the origin.

%C 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.

%C The asymptotical ratio of odd to even powerful numbers (Srichan, 2020). - _Amiram Eldar_, Mar 07 2021

%C 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

%H G. C. Greubel, <a href="/A101465/b101465.txt">Table of n, a(n) for n = 0..10000</a>

%H Mireille Bousquet-Mélou and Gilles Schaeffer, <a href="https://doi.org/10.1007/s004400200205">Walks on the slit plane</a>, Probability Theory and Related Fields, Vol. 124, No. 3 (2002), pp. 305-344; <a href="http://arxiv.org/abs/math/0012230">arXiv preprint</a>, arXiv:0012230 [math.CO], 2000.

%H Mathematical Reflections, <a href="https://www.awesomemath.org/wp-pdf-files/math-reflections/mr-2014-05/mr_4_2014_solutions.pdf">Solution to Problem J307</a>, Issue 5, 2014, p. 21.

%H Moreton Moore, <a href="http://www.jstor.org/stable/3615957">Symmetrical Intersections of Right Circular Cylinders</a>, The Mathematical Gazette, Vol. 58, No. 405 (1974), pp. 181-185.

%H Teerapat Srichan, <a href="http://www.math.nthu.edu.tw/~amen/2020/AMEN-200219.pdf">The Odd/Even Dichotomy For The Set Of Square-Full Numbers</a>, Applied Mathematics E-Notes, Vol. 20 (2020), pp. 528-531.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Octagon.html">Octagon</a>.

%e 0.585786437626904951198311275790301921430328124623051926823320262...

%t RealDigits[2 - Sqrt[2], 10, 100][[1]] (* _G. C. Greubel_, Oct 01 2018 *)

%o (PARI) 2 - sqrt(2) \\ _Michel Marcus_, Jan 07 2017

%o (Magma) SetDefaultRealField(RealField(100)); 2 - Sqrt(2); // _G. C. Greubel_, Oct 01 2018

%Y Cf. A001694, A002193 (sqrt(2)).

%K cons,nonn

%O 0,1

%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 20 2005