A076415 Decimal expansion of second solution of the equation cos(x)*cosh(x) = 1.

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

Offset

1,1

Comments

This is an equation related to a beam clamped at both ends: cos(x)*cosh(x) = 1. The first three solutions are: 4.73 (A076414), 7.853 (this sequence) and 10.996 (A076416).

Links

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

Z. Guede and I. Elishakov, A fifth-order polynomial that serves as both.., Chaos, Solitons and Fractals 12 (2001) 1267-1298.

Index entries for transcendental numbers.

Example

cos(x)*cosh(x) = 1, x = 7.8532...

Maple

Digits:= 120:
fsolve(cos(x)*cosh(x)-1, x=8);  # Alois P. Heinz, Apr 14 2026

Mathematica

RealDigits[x/.FindRoot[Cos[x] Cosh[x]==1, {x, 5 Pi/2}, WorkingPrecision->120]][[1]] (* Jean-François Alcover, Mar 14 2011 *)

Prog

(PARI) solve(x=7, 8, cos(x)*cosh(x)-1) \\ Charles R Greathouse IV, May 17 2026

Crossrefs

Cf. A076414, A076416.

Sequence in context: A109916 A277053 A370466 * A190573 A216542 A216544

Adjacent sequences: A076412 A076413 A076414 * A076416 A076417 A076418

Keyword

easy,nonn,cons

Author

Zak Seidov, Oct 10 2002

Status

approved