[seqfan] Re: A051264 == A050278 ?

Hans Havermann gladhobo at teksavvy.com
Mon Jan 9 22:36:57 CET 2012

Franklin T. Adams-Watters:

> Can anyone access the book "More Mathematical Morsels" by R.  
> Honsberger, referenced in the MathWorld article? It presumably has a  
> definition of n-persistent, and as the published version, we should  
> match it.

"If a positive integer k contains all ten digits, 0, 1, 2,..., 9, and  
this property persists through all its multiples k, 2k, 3k,..., then k  
is said to be a persistent number. It turns out that there are no  
persistent numbers: the demand for persistence through all multiples  
is just too much to ask. An unbroken initial run of successes,  
however, does not go unrecognized; if the first n multiples k, 2k,...,  
nk, each contain all ten digits, then k is awarded the distinction of  
being called n-persistent. For example, k = 1234567890 is 2-persistent  
because 2k = 2469135780, but not 3-persistent, in view of 3k =  

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