A072508 Decimal expansion of Backhouse constant.

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

Offset

1,2

Comments

The reciprocal (A088751) of Backhouse's constant is the real zero of a certain power series. - T. D. Noe, Oct 14 2003

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=1..105.

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]

Simon Plouffe, The Backhouse constant.

Eric Weisstein's World of Mathematics, Backhouse's Constant.

Example

1.4560749485826896713995953...

Mathematica

RealDigits[-1/x /. FindRoot[0 == 1 + Sum[x^n Prime[n], {n, 1000}], {x, {0, 1}}, WorkingPrecision -> 100]][[1]] (* T. D. Noe, corrected Apr 26 2013 *)

Crossrefs

Continued fraction is in A074269.

Cf. A030010, A088751, A247818.

Sequence in context: A344024 A327703 A077061 * A075566 A348355 A076087

Adjacent sequences: A072505 A072506 A072507 * A072509 A072510 A072511

Keyword

cons,nonn

Author

Robert G. Wilson v, Aug 03 2002

Status

approved