A120219 Decimal expansion of sole real negative fixed point of Sum[x^Prime[n+1],{n,0,Infinity}].

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

Offset

0,1

Comments

Only other fixed points are 0 and A120220. Function involved is equivalent to o.g.f. Sum[A010051(n)*x^n, {n, 0, Infinity}] where A010051(0) is considered 0.

Links

Table of n, a(n) for n=0..104.

Example

-0.8267323144...

Mathematica

Select[NSolve[Sum[x^Prime[n + 1], {n, 0, (*arb*)250}] == x, x, (*arb*)80], Element[ #[[1]][[2]], Reals] && Negative[ #[[1]][[2]]] &][[1]][[1]][[2]]

Prog

(PARI) default(realprecision, 180); solve(x=-0.83, -0.82, sum(i=0, 400, x^(prime(i+1)))-x) \\ Robert Gerbicz, May 08 2008

Crossrefs

Cf. A120220.

Sequence in context: A322129 A019635 A011468 * A367899 A240976 A377400

Adjacent sequences: A120216 A120217 A120218 * A120220 A120221 A120222

Keyword

cons,nonn

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 10 2006

Extensions

More terms from Robert Gerbicz, May 08 2008

Corrected by Arkadiusz Wesolowski, Aug 17 2011

Status

approved