A069995 Decimal expansion of the real positive solution to zeta(x)=x.

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

Offset: 1

Author

Benoit Cloitre, May 01 2002

Keywords

• cons
• easy
• nonn

Comments

Fixed point of Riemann zeta function. - Michal Paulovic, Dec 31 2017

Examples

			1.83377265168027139624564858944152359218097851880099333719403756009807267200...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• David Rainford, Riemann zeta function: iteration of ζ and the significance of the value 1.83377..., Prime Patterns, 2015.
• David Rainford, Hurwitz zeta function: iteration fractal example near a threshold, Prime Patterns, 2019. [observed effects of tangent to fixed-point curve]

Crossrefs

Cf. A069857, A324859, A324860.

Programs

Mathematica

RealDigits[ FindRoot[ Zeta[x] == x, {x, 2}, WorkingPrecision -> 2^7, AccuracyGoal -> 2^8, PrecisionGoal -> 2^7][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v, Jan 07 2018 *)

PARI

solve(x=1.5,2,zeta(x)-x) \\ Michal Paulovic, Dec 31 2017

Sage

(zeta(x)==x).find_root(1,2,x) # G. C. Greubel, Apr 01 2019

Extensions

Corrected and extended by Michal Paulovic, Dec 31 2017