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

0,1

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 that of Backhouse's constant.

References

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

Links

Table of n, a(n) for n=0..99.

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.

Example

0.68677783446063...

Mathematica

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

Crossrefs

Cf. A030010, A072508.

Sequence in context: A339606 A360928 A200326 * A153627 A094540 A010724

Adjacent sequences: A088748 A088749 A088750 * A088752 A088753 A088754

Keyword

cons,nonn

Author

T. D. Noe, Oct 14 2003

Status

approved