%I #25 Mar 13 2018 03:51:05
%S 2,3,7,1,4,5,0,6,6,0,3,3,8,3,9,3,2,6,1,1,8,5,9,0,5,2,1,1,9,5,4,8,9,1,
%T 6,5,1,7,8,1,3,1,9,5,7,2,1,0,3,6,3,6,2,3,4,3,8,0,1,7,0,8,9,6,0,8,5,8,
%U 8,0,2,4,6,3,6,3,8,3,1,6,3,0,2,5,4,2,0,2,5,6,5,4,7,5,0,4,9,8,7,4,8,3,8,2,1
%N Decimal expansion of the fifth smallest positive real root of sin(x) - sin(x^3) = 0.
%C Let c(n) be defined as the smallest solution to sin(x) = sin(x^n); then lim_{n -> infinity} c(n) = C = 2.36338112904... = w004 in Plouffe's inverter.
%F Let x = (3*(45*Pi+sqrt(3*(4+675*Pi^2))))^(1/3) then the constant is (2^(1/3)*x^2-6)/(3*2^(2/3)*x). - _Peter Luschny_, Mar 12 2018
%t Root[#^3 + # - 5*Pi&, 1] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Mar 04 2013 *)
%o (PARI) solve(x=2.3, 2.4, sin(x) - sin(x^3)) \\ _Michel Marcus_, Mar 11 2018
%K easy,nonn,cons
%O 1,1
%A _Benoit Cloitre_, Mar 30 2002
%E Name clarified by _Peter Luschny_, Mar 12 2018