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Decimal expansion of the fifth smallest positive real root of sin(x) - sin(x^3) = 0.
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%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