|
%I #45 Apr 11 2024 15:08:05
%S 2,0,7,9,4,4,1,5,4,1,6,7,9,8,3,5,9,2,8,2,5,1,6,9,6,3,6,4,3,7,4,5,2,9,
%T 7,0,4,2,2,6,5,0,0,4,0,3,0,8,0,7,6,5,7,6,2,3,6,2,0,4,0,0,2,8,4,8,0,1,
%U 8,0,8,6,5,9,0,9,0,8,4,1,4,6,8,1,7,5,8,9,9,8,0,9,8,9,2,5,6,0,6
%N Decimal expansion of log(8).
%C a(n+1) is also the sequence of digits in the base-ten expansion of the number representing the probability that an acute triangle could be formed with the pieces obtained by breaking a stick into three parts at random. The breaking points are chosen with uniform distribution and independently of one another. - _Eugen J. Ionascu_, Feb 19 2011
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.
%D Bruce C. Berndt, Ramanujan's Notebooks Part I, Springer-Verlag.
%H Harry J. Smith, <a href="/A016631/b016631.txt">Table of n, a(n) for n = 1..20000</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H Eugen J. Ionascu and Gabriel Prajitura, <a href="http://arxiv.org/abs/1009.0890">Things to do with a broken stick</a>, arXiv:1009.0890 [math.HO], 2010-2013.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 2 + Sum_{n >= 1} 1/( n*(16*n^2 - 1) ). This summation was the first problem submitted by Ramanujan to the Journal of the Indian Mathematical Society. See Berndt, Corollary on p. 29. - _Peter Bala_, Feb 25 2015
%F Equals 2 + Sum_{n >= 1} (-1)^n*(n-1)/(n*(n+1)). - _Bruno Berselli_, Sep 09 2020
%F Equals 2 + Sum_{k>=1} zeta(2*k+1)/16^k. - _Amiram Eldar_, May 27 2021
%F Equals 3*A002162. - _R. J. Mathar_, Apr 11 2024
%e 2.079441541679835928251696364374529704226500403080765762362040028480180....
%p a:=proc(n)
%p local x,y,z,w;
%p Digits:=2*n+1;
%p x:=3*ln(2);y:=floor(10^(n-2)*x)*10;
%p z:=floor(10^(n-1)*x);w:=z-y;
%p end: # _Eugen J. Ionascu_, Feb 19 2011
%t RealDigits[Log[8], 10, 90][[1]] (* _Bruno Berselli_, Mar 26 2013 *)
%o (PARI) default(realprecision, 20080); x=log(8); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016631.txt", n, " ", d)); \\ _Harry J. Smith_, May 16 2009
%Y Cf. A016736 (continued fraction). - _Harry J. Smith_, May 16 2009
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_
|
