A076417 - OEIS

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A076417

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

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

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OFFSET

1,2

COMMENTS

This is an equation related to a cantilever beam: cos(x)*cosh(x) = -1. The first three solutions are: 1.875 (this sequence), 4.69409 (A076418) and 7.854757 (A076419).

LINKS

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

Z. Guede, 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

1.87510406871196116644530824107821416257011173353...

MATHEMATICA

RealDigits[x/.FindRoot[Cos[x]Cosh[x]==-1, {x, 1.8}, WorkingPrecision->120], 10, 120][[1]] (* Harvey P. Dale, Jul 24 2011 *)

PROG

(PARI) solve(x=1, 2, cos(x)*cosh(x) + 1) \\ Michel Marcus, Sep 11 2019

CROSSREFS

Cf. A009398, A076418, A076419.

Cf. A005981, A058258, A008775.