

A120219


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


1



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



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 * A240976 A199158 A086089
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



