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

Author

Robert G. Wilson v, Aug 03 2002

Keywords

• cons
• nonn

Comments

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

Examples

			1.4560749485826896713995953...
		

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]
• Simon Plouffe, The Backhouse constant.
• Eric Weisstein's World of Mathematics, Backhouse's Constant.

Crossrefs

Continued fraction is in A074269.

Cf. A030010, A088751, A247818.

Programs

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 *)