A120220 Decimal expansion of sole real positive fixed point of Sum_{n>=0} x^Prime(n+1).

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

Offset

0,1

Comments

Only other fixed points are 0 and A120219. Function involved is equivalent to o.g.f. Sum_{n>0} A010051(n)*x^n, where A010051(0) is considered 0.

Links

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

Example

0.55785865376795666357725966112536889754852239689...

Maple

Digits := 160 ; nmax := 3*Digits ; fx := -x; p := 2; while p < nmax do fx := fx + x^p ; p := nextprime(p) ; od: fxp := diff(fx, x) ; y := 0.557 ; for i from 1 to 100 do y := y-eval(fx, x=y)/eval(fxp, x=y) ; printf("%.120f\n", y) ; od: # R. J. Mathar, May 19 2009

Mathematica

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

Crossrefs

Cf. A120219.

Sequence in context: A053671 A028278 A095943 * A320639 A153105 A201523

Adjacent sequences: A120217 A120218 A120219 * A120221 A120222 A120223

Keyword

cons,hard,nonn

Author

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

Extensions

More digits from R. J. Mathar, May 19 2009

Status

approved