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%I #9 Jan 26 2023 12:31:50
%S 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,
%T 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,
%U 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
%N Decimal expansion of sole real negative fixed point of Sum[x^Prime[n+1],{n,0,Infinity}].
%C 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.
%e -0.8267323144...
%t 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]]
%o (PARI) default(realprecision,180);solve(x=-0.83,-0.82,sum(i=0,400,x^(prime(i+1)))-x) \\ _Robert Gerbicz_, May 08 2008
%Y Cf. A120220.
%K cons,nonn
%O 0,1
%A Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 10 2006
%E More terms from _Robert Gerbicz_, May 08 2008
%E Corrected by _Arkadiusz Wesolowski_, Aug 17 2011