- References
| Binary | 1.01110100110000010101001111101100… |
| Decimal | 1.45607494858268967139959535111654… |
| Hexadecimal | 1.74C153ECB002353B12A0E476D3ADD… |
| Continued fraction |  |
Backhouse's constant is a mathematical constant named after Nigel Backhouse. Its value 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 its multiplicative inverse as a formal power series,
Then:
{{OEIS|id=A072508}}.
This limit was conjectured to exist by {{harvtxt|Backhouse|1995}}, and the conjecture was later proven by {{harvs|first=Philippe|last=Flajolet|authorlink=Philippe Flajolet|year=1995|txt}}.
References
- {{citation|first=N.|last=Backhouse|title=Formal reciprocal of a prime power series|series=unpublished note|year=1995}}
- {{citation|first=Philippe|last=Flajolet|authorlink=Philippe Flajolet|title=On the existence and the computation of Backhouse's constant|series=Unpublished manuscript|date=November 25, 1995}}. Reproduced in Les cahiers de Philippe Flajolet, Hsien-Kuei Hwang, June 19, 2014, accessed 2014-12-06.
- {{mathworld|title=Backhouse's Constant|urlname=BackhousesConstant}}
- {{Cite OEIS|A030018}}
- {{Cite OEIS|A074269}}
- {{Cite OEIS|A088751}}
2 : Mathematical constants|Prime numbers
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