A068353 Decimal expansion of smallest positive root of cos(Pi x/2) cosh(Pi x/2) = -1.

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

Offset

1,3

Comments

The root is x = 1.1937283253889343234388...

References

Harrington, E. A. (1928). The vibrations of tuning-forks. JOSA, 17, 224-237.

Keulegan, G. H. (1928). On the vibration of U bars (Doctoral dissertation, Johns Hopkins University).

Liebetrau, A. M. (1979). Some tests of randomness based upon the variance-time curve of the Poisson process. Journal of the Royal Statistical Society. Series B (Methodological), 41, 32-39.

Links

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

Mathematica

RealDigits[FindRoot[Cos[Pi x/2]Cosh[Pi x/2]==-1, {x, 1}, WorkingPrecision->200][[1, 2]]][[1]]

Prog

(PARI) solve(x=1, 2, cos(x)*cosh(x)+1)*2/Pi \\ Charles R Greathouse IV, Apr 16 2014

Crossrefs

Equals (2/Pi) times A076417.

Sequence in context: A011390 A011229 A324993 * A346989 A136251 A073002

Adjacent sequences: A068350 A068351 A068352 * A068354 A068355 A068356

Keyword

nonn,cons

Author

Joost de Winter, Feb 28 2002

Extensions

Edited by Dean Hickerson, Jun 07 2002

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

Status

approved