A076422 Decimal expansion of third solution of equation tan(x) = tanh(x).

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

Offset

2,3

Comments

This is an equation related to a beam clamped at left and simply supported at right: tan(x) = tanh(x). The first three solutions are: 3.927... (A076420), 7.069... (A076421) and 10.21... (this sequence).

Links

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

Zakoua Guédé and Isaac Elishakoff, 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

10.2101761228130305454682055946565398249530579895513...

Mathematica

RealDigits[x /. FindRoot[Tan[x] == Tanh[x], {x, 10}, WorkingPrecision->120], 10, 105][[1]] (* Amiram Eldar, May 02 2023 *)

Prog

(PARI) solve(x = 10, 10.3, tan(x) - tanh(x)) \\ Amiram Eldar, May 02 2023

Crossrefs

Cf. A076420, A076421.

Sequence in context: A217653 A331161 A176887 * A295861 A337272 A058998

Adjacent sequences: A076419 A076420 A076421 * A076423 A076424 A076425

Keyword

easy,nonn,cons

Author

Zak Seidov, Oct 10 2002

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009

Status

approved