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

Author

Benoit Cloitre, Jun 19 2002

Keywords

• base
• cofr
• easy
• nonn

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

Crossrefs

Cf. A069857 (decimal expansion).

Programs

PARI

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

Extensions

Offset changed by Andrew Howroyd, Jul 06 2024