[seqfan] Re: Remeven numbers
user42_kevin at yahoo.com.au
Mon Jan 6 10:04:53 CET 2020
mlb at well.com (Marc LeBrun) writes:
> "A positive integer is remeven just if the remainder is always even
> whenever it's divided by any of its decimal digits."
In that form (A330981 and A330982) the digit strings are a regular
language (like many/most combinations of digits and divisible-ness).
On a quick attempt I make a minimized DFA state machine for remeven
having 2763 states, or remodd having 924 states.
(These are upper bounds on the order of a linear recurrence for how
many remeven/remodd of given digit length, and so what index n has
the first of given digit length. Going naively from 2763 states to
a recurrence may need a computer with a bit of grunt ...)
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