Backhouse's constant

Backhouse's constant is a mathematical constant founded by N. Backhouse and is approximately 1.456 074 948.

It is defined by using the power series such that the coefficients of successive terms are the prime numbers:

and where

Then:

(sequence A072508 in OEIS).

The limit was conjectured to exist by Backhouse which was later proved by P. Flajolet.

Binary 1.01110100110000010101001111101100…
Decimal 1.45607494858268967139959535111654…
Hexadecimal 1.74C153ECB002353B12A0E476D3ADD…
Continued fraction

Note that this continued fraction is not periodic.

References

* Weisstein, Eric W., "Backhouse's Constant" from MathWorld.
* A030018, A074269, A088751

Mathematical Constants