A076416 - OEIS

A076416

Decimal expansion of third solution of equation cos(x)*cosh(x) = 1.

1, 0, 9, 9, 5, 6, 0, 7, 8, 3, 8, 0, 0, 1, 6, 7, 0, 9, 0, 6, 6, 6, 9, 0, 3, 2, 5, 1, 9, 1, 0, 5, 8, 9, 2, 4, 1, 7, 5, 4, 2, 8, 0, 3, 0, 3, 0, 5, 7, 6, 3, 6, 1, 9, 9, 7, 0, 7, 6, 5, 5, 5, 9, 0, 2, 6, 5, 6, 9, 2, 2, 8, 2, 8, 9, 0, 0, 2, 8, 7, 1, 2, 0, 3, 7, 6, 1, 7, 8, 7, 6, 2, 0, 2, 3, 5, 3, 4, 9, 8, 2, 7, 7, 9, 9

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OFFSET

2,3

COMMENTS

This is an equation related to a beam clumped at both ends: cos(x) cosh(x) = 1. The first three solutions are: 4.73 (A076414), 7.853 (A076415) and 10.9956 (this sequence).

LINKS

Table of n, a(n) for n=2..106.

Z. Guede and I. Elishakov, A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure, Chaos, Solitons and Fractals 12 (7) (2001) 1267-1298.

EXAMPLE

10.995607838001670906669...

MATHEMATICA

RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1, {x, 7 Pi/2}, WorkingPrecision -> 120]][[1]] (* Jean-François Alcover, Mar 14 2011 *)

PROG

(PARI) solve(x=9, 11, cos(x)*cosh(x)-1) \\ Charles R Greathouse IV, Mar 15 2011

CROSSREFS

Cf. A076414, A076415.

Sequence in context: A347081 A347152 A131744 * A201289 A091133 A334452