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

0,1

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

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

Sequence in context: A366163 A358630 A100610 * A010719 A246903 A213022

Adjacent sequences: A101462 A101463 A101464 * A101466 A101467 A101468

Keyword

cons,nonn

Author

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

Status

approved