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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
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.
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
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