A068960 Decimal expansion of the fifth smallest positive real root of sin(x) - sin(x^3) = 0.

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, 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, 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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..105.

Formula

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

Mathematica

Root[#^3 + # - 5*Pi&, 1] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Mar 04 2013 *)

Prog

(PARI) solve(x=2.3, 2.4, sin(x) - sin(x^3)) \\ Michel Marcus, Mar 11 2018

Crossrefs

Sequence in context: A083521 A104691 A011160 * A358969 A205129 A236290

Adjacent sequences: A068957 A068958 A068959 * A068961 A068962 A068963

Keyword

easy,nonn,cons

Author

Benoit Cloitre, Mar 30 2002

Extensions

Name clarified by Peter Luschny, Mar 12 2018

Status

approved