login
Decimal expansion of 4+2*sqrt(5).
2

%I #5 Sep 08 2018 12:25:06

%S 8,4,7,2,1,3,5,9,5,4,9,9,9,5,7,9,3,9,2,8,1,8,3,4,7,3,3,7,4,6,2,5,5,2,

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

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

%N Decimal expansion of 4+2*sqrt(5).

%C Continued fraction expansion of 4+2*sqrt(5) is A010698 preceded by 8.

%C a(n) = A010476(n) = A020762(n-1) = A134974(n) for n > 1.

%C Rajan (2010) claims the variance of a discrete distribution generated by the linear convolution of Fibonacci sequence with itself, saturates to a constant of value 8.4721359. [From _Jonathan Vos Post_, May 10 2010]

%H Arulalan Rajan, Jamadagni, Vittal Rao, Ashok Rao, <a href="http://arxiv.org/abs/1005.1231">Convolutions Induced Discrete Probability Distributions and a New Fibonacci Constant</a>, May 6, 2010. [From _Jonathan Vos Post_, May 10 2010]

%e 4+2*sqrt(5) = 8.47213595499957939281...

%t RealDigits[4+2Sqrt[5],10,120][[1]] (* _Harvey P. Dale_, Sep 08 2018 *)

%Y Cf. A002163 (decimal expansion of sqrt(5)), A010476 (decimal expansion of sqrt(20)), A020762 (decimal expansion of 1/sqrt(5)), A134974 (decimal expansion of 8/(1+sqrt(5))), A010698 (repeat 2, 8).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 20 2010