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A088751 Decimal expansion of -x, the real root of the equation 0 = 1 + Sum_{k>=1} prime(k) x^k. The inverse of Backhouse's constant (A072508).

%I A088751 #31 Feb 16 2025 08:32:51
%S A088751 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,
%T A088751 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,
%U A088751 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
%N A088751 Decimal expansion of -x, the real root of the equation 0 = 1 + Sum_{k>=1} prime(k) x^k. The inverse of Backhouse's constant (A072508).
%C A088751 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 that of Backhouse's constant.
%D A088751 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.5, p. 294.
%H A088751 S. R. Finch, <a href="/A104225/a104225.pdf">Backhouse's constant</a>, 1995. [Cached copy, with permission]
%H A088751 Philippe Flajolet, in response to the previous document from S. R. Finch, <a href="/A104225/a104225.txt">Backhouse's constant</a>, 1995.
%H A088751 S. R. Finch, <a href="/A104225/a104225_1.pdf">Kalmar's Composition Constant</a>, Section 5.5 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 292-295, 2003. [Cached copy, with permission]
%H A088751 S. R. Finch, <a href="/A001055/a001055.pdf">Kalmar's composition constant</a>, June 5, 2003. [A different version. Cached copy, with permission of the author]
%H A088751 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BackhousesConstant.html">Backhouse's Constant</a>.
%e A088751 0.68677783446063...
%t A088751 RealDigits[ -x/.FindRoot[0==1+Sum[x^n Prime[n], {n, 1000}], {x, {0, 1}}, WorkingPrecision->100]][[1]]
%Y A088751 Cf. A030010, A072508.
%K A088751 cons,nonn
%O A088751 0,1
%A A088751 _T. D. Noe_, Oct 14 2003