

A088751


Decimal expansion of x, the real root of the equation 0 = 1 + Sum{k=1,infinity} prime(k) x^k. The inverse of Backhouse's constant (A072508).


3



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

0,1


COMMENTS

This constant is computed in Finch's article. This number is easier to compute than Backhouse's constant. Except for an additional term of 0, the continued fraction expansion is the same as Backhouse's constant.


LINKS

Table of n, a(n) for n=0..99.
S. R. Finch, Kalmar's Composition Constant
Eric Weisstein's World of Mathematics, Backhouse's Constant


EXAMPLE

0.68677783446063...


MATHEMATICA

RealDigits[ x/.FindRoot[0==1+Sum[x^n Prime[n], {n, 1000}], {x, {0, 1}}, WorkingPrecision>100]][[1]]


CROSSREFS

Cf. A072508.
Sequence in context: A021597 A169685 A200326 * A153627 A094540 A010724
Adjacent sequences: A088748 A088749 A088750 * A088752 A088753 A088754


KEYWORD

cons,nonn


AUTHOR

T. D. Noe, Oct 14 2003


STATUS

approved



