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%I #12 May 13 2014 21:00:26
%S 4,7,3,0,0,4,0,7,4,4,8,6,2,7,0,4,0,2,6,0,2,4,0,4,8,1,0,0,8,3,3,8,8,4,
%T 8,1,9,8,9,8,3,4,1,8,0,0,7,0,6,8,4,8,6,8,9,0,9,6,3,5,5,8,4,5,3,6,9,1,
%U 3,6,6,6,9,8,5,2,0,1,3,1,8,2,1,8,1,9,5,4,8,9,3,9,2,7,3,2,0,9,1,6,5,8,5,9,1
%N Decimal expansion of first solution of equation cos(x) cosh(x) = 1.
%C This is an equation related to a beam clumped at both ends: cos(x) cosh(x) = 1. The first three solutions are: 4.73 (this sequence), 7.853 (A076415) and 10.996 (A076416).
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 221.
%H Z. Guede, I. Elishakov, <a href="http://dx.doi.org/10.1016/S0960-0779(00)00014-X">A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure</a>, Chaos, Solitons and Fractals 12 (7) (2001) 1267-1298.
%e cos(x) cosh(x) = 1, x = 4.73004.
%t RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1,{x,3 Pi/2},WorkingPrecision -> 120]][[1,1;;105]] (* Jean-Francois Alcover, Mar 14 2011 *)
%Y Cf. A076415, A076416.
%K easy,nonn,cons
%O 1,1
%A _Zak Seidov_, Oct 10 2002
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