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).

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

Offset: 0

Author

T. D. Noe, Oct 14 2003

Keywords

• cons
• nonn

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 that of Backhouse's constant.

Examples

			0.68677783446063...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.5, p. 294.

Links

• S. R. Finch, Backhouse's constant, 1995. [Cached copy, with permission]
• Philippe Flajolet, in response to the previous document from S. R. Finch, Backhouse's constant, 1995.
• S. R. Finch, Kalmar's Composition Constant, Section 5.5 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 292-295, 2003. [Cached copy, with permission]
• S. R. Finch, Kalmar's composition constant, June 5, 2003. [A different version. Cached copy, with permission of the author]
• Eric Weisstein's World of Mathematics, Backhouse's Constant.

Crossrefs

Cf. A030010, A072508.

Programs

Mathematica

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