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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 in [[arithmetic progression]]; the factors fall into the pattern

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

(contracted; show full)

Other Carmichael numbers of that kind are: 294409, 56052361, 118901521, 172947529, 216821881, 228842209, 1299963601, 2301745249, 9624742921, …

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.

==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]]
[[fi:Zeiselin luku]]
[[it:Numero di Zeisel]]