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Zeisel number
A '''Zeisel number''', named after [[Helmut Zeisel]], is a [[square-free integer]] ''k'' with at least three [[prime factor]]s which fall into the pattern

:<math>p_x = ap_{x - 1} + b</math>

(contracted; show full)

The name Zeisel numbers was probably introduced by Kevin Brown, who was looking for numbers that when plugged into the equation 

:<math>2^{k - 1} + k</math> 

yield [[prime number]]s. In a posting to the [[newsgroup]] sci.math on 1994-02-24, Helmut Zeisel pointed out that 1885 is one such number. Later it was discovered (by Kevin Brown?) that 1885 additionally has prime factors with the relationship described above, so a name like Brown-Zeisel Numbers might be more appropriate.

Hardy
  –Ramanujan's number [[1729 (number)|1729]] is also a Zeisel number.

==Notes==
{{reflist}}

==External links==
*[[Wikisource:Zeisel numbers]]
*{{MathWorld|urlname=ZeiselNumber|title=Zeisel Number}}
*[http://www.mathpages.com/home/kmath015.htm MathPages article]

{{Classes of natural numbers}}

[[Category:Integer sequences]]