cp's OEIS Frontend

A101465 Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.

%I A101465 #63 Aug 24 2025 19:42:56
%S A101465 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 A101465 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 A101465 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 A101465 Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.
%C A101465 This also equals the probability, for a random walk on the slit plane starting at (1,0), of stopping at the origin.
%C A101465 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 A101465 The asymptotical ratio of odd to even powerful numbers (Srichan, 2020). - _Amiram Eldar_, Mar 07 2021
%C A101465 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
%C A101465 Smallest root of the Laguerre polynomial of degree 2. - _A.H.M. Smeets_, May 15 2025
%H A101465 G. C. Greubel, <a href="/A101465/b101465.txt">Table of n, a(n) for n = 0..10000</a>
%H A101465 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 A101465 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 A101465 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 A101465 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 A101465 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Octagon.html">Octagon</a>.
%H A101465 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%e A101465 0.585786437626904951198311275790301921430328124623051926823320262...
%t A101465 RealDigits[2 - Sqrt[2], 10, 100][[1]] (* _G. C. Greubel_, Oct 01 2018 *)
%o A101465 (PARI) 2 - sqrt(2) \\ _Michel Marcus_, Jan 07 2017
%o A101465 (Magma) SetDefaultRealField(RealField(100));  2 - Sqrt(2); // _G. C. Greubel_, Oct 01 2018
%Y A101465 Cf. A001694, A002193 (sqrt(2)).
%K A101465 cons,nonn,changed
%O A101465 0,1
%A A101465 Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 20 2005