A163960 Decimal expansion of 2*(sqrt(2) - 1).

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

Offset: 0

Author

N. J. A. Sloane, Oct 02 2010

Keywords

• nonn
• cons

Comments

Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(1,1,sqrt(2)). (See A195284.) - Clark Kimberling, Sep 14 2011

Examples

			0.82842712474619009760337744841939615713934375075389614635335...
		

References

• J. M. Steele, Probability Theory and Combinatorial Optimization, SIAM, 1997, p. 3.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A084158, A156035, A195284.

Essentially the same digit sequence as A010466, A086178, A090488 and A157258.

Programs

Mathematica

RealDigits[2(Sqrt[2]-1),10,120][[1]] (* Harvey P. Dale, May 27 2016 *)

PARI

2*(sqrt(2)-1) \\ G. C. Greubel, Aug 13 2017

Formula

Equals Sum_{k>=0} (-1)^k * binomial(2*k,k)/((k+1) * 4^k). - Amiram Eldar, May 06 2022

Equals Sum_{k>=1} (-1)^(k+1)/A084158(k). - Amiram Eldar, Dec 02 2024