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

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, 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, 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

Offset: 0

Author

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

Keywords

• cons
• nonn
• changed

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

Smallest root of the Laguerre polynomial of degree 2. - A.H.M. Smeets, May 15 2025

Examples

			0.585786437626904951198311275790301921430328124623051926823320262...
		

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.
• Index entries for algebraic numbers, degree 2.

Crossrefs

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

Programs

Magma

SetDefaultRealField(RealField(100));  2 - Sqrt(2); // G. C. Greubel, Oct 01 2018

Mathematica

RealDigits[2 - Sqrt[2], 10, 100][[1]] (* G. C. Greubel, Oct 01 2018 *)

PARI

2 - sqrt(2) \\ Michel Marcus, Jan 07 2017