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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)

:<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 is also a Zeisel number.


Chernick numbers (named after Jack Chernick)<ref>{{cite journal |author=Chernick, J. |year=1939 |title=On Fermat's simple theorem |journal=Bull. Amer. Math. Soc. |volume=45 |pages=269–274 |doi=10.1090/S0002-9904-1939-06953-X  |url=http://www.ams.org/journals/bull/1939-45-04/S0002-9904-1939-06953-X/S0002-9904-1939-06953-X.pdf}}</ref> are a subset of [[Carmichael number]]s (named after [[Robert Carmichael]]) which are a subset of Zeisel numbers.⏎
⏎
==Notes==
{{reflist}}

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

[[Category:Integer sequences]]

[[fr:Nombre de Zeisel]]
[[it:Numero di Zeisel]]
[[ja:ツァイゼル数]]
[[fi:Zeiselin luku]]