A163960 - OEIS

%I #25 Feb 07 2025 12:38:05

%S 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,

%T 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,

%U 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

%N Decimal expansion of 2*(sqrt(2) - 1).

%C 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

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

%H G. C. Greubel, <a href="/A163960/b163960.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

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

%F Equals Sum_{k>=1} (-1)^(k+1)/A084158(k). - _Amiram Eldar_, Dec 02 2024

%e 0.82842712474619009760337744841939615713934375075389614635335...

%t RealDigits[2(Sqrt[2]-1),10,120][[1]] (* _Harvey P. Dale_, May 27 2016 *)

%o (PARI) 2*(sqrt(2)-1) \\ _G. C. Greubel_, Aug 13 2017

%Y Cf. A084158, A156035, A195284.

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

%K nonn,cons,changed

%O 0,1

%A _N. J. A. Sloane_, Oct 02 2010