A072115 Continued fraction expansion of abs(C) where C=-0.2959050055752...is the real negative solution to zeta(x)=x.

0, 3, 2, 1, 1, 1, 2, 1, 7, 14, 1, 2, 10, 1, 5, 3, 1, 7, 2, 1, 2, 2, 2, 4, 1, 1, 12, 1, 1, 1, 14, 2, 10, 3, 5, 6, 2, 1, 6, 13, 1, 2, 2, 4, 8, 1, 4, 8, 2, 1, 16, 1, 1, 1, 1, 4, 2, 1, 1, 1, 3, 13, 4, 1, 2, 1, 6, 1, 1, 2, 43, 1, 3, 1, 1, 2, 2, 2, 1, 2, 2, 2, 10, 5, 4, 8, 1, 5, 3, 2, 1, 1, 3, 2, 19

Offset

0,2

Comments

Start from any complex number z=x+iy, not solution to zeta(z)=z, iterate the zeta function on z. If zeta_m(z) (=zeta(zeta(....(z)..)) m times) has a limit when m grows, then this limit seems to always be the real number : C=-0.2959050055752....Example: if z=3+5I after 30 iterations : zeta_30(z)=-0.29590556499...-0.00000041029065...*I

Links

Table of n, a(n) for n=0..94.

Prog

(PARI) \p150 contfrac(abs(solve(X=-1, 0, zeta(X)-X)))

Crossrefs

Cf. A069857 (decimal expansion).

Sequence in context: A073572 A073356 A093032 * A210650 A218754 A079948

Adjacent sequences: A072112 A072113 A072114 * A072116 A072117 A072118

Keyword

base,cofr,easy,nonn

Author

Benoit Cloitre, Jun 19 2002

Extensions

Offset changed by Andrew Howroyd, Jul 06 2024

Status

approved