# [seqfan] definition of pandigital numbers & related issues

Maximilian Hasler maximilian.hasler at gmail.com
Thu May 27 19:35:51 CEST 2010

```Dear SeqFans,

sequence

http://oeis.org/classic/A050278
Pandigital numbers: numbers containing the digits 0-9.

has the keyword "fini", corresponding (probably) to the more precise definition
"numbers containing each of the digits 0-9 exactly once."

However, most(?) other instances of "pandigital" in OEIS do not imply
In particular, the xref'd
A050288  	 	 Pandigital primes.
would not be possible (*), and the sequence's author's "own" page
http://mathworld.wolfram.com/PandigitalNumber.html
does not necessarily include this restriction in the definition.
Also
A050290  	 	 Zeroless pandigital primes,
from the same author, does not use this restriction.

So I think the simplest solution would be to remove the kw "fini".
But I just submit this idea for consideration, don't want to decide

(*) in view of A. Del Arte's post from March and his page
http://oeis.org/wiki/Classifications_of_prime_numbers#By_representation_in_specific_bases
one might add "decimal" or "base 10", when this is meant but not made
explicit, as in A050288.

Sequence
A140532  	 	 a(n) = number of n-digit pandigital primes.
seems to use still another definition of "pandigital" ---
another term should be found for this, it (probably(?)) refers to
A029743  	 	 Primes with distinct digits.
complement of
A073064  	 	 Primes with non-distinct digits. ).
(and in the example for A140532, "+" could be replaced by ",")

Related issue:

A159474  	 	 Pandigital primes with least digit sum (46) starting with
the largest and listed in descending order.

seems incorrect to me ; unless I oversee something, these can be
arbitrarily large ; e.g.
908765421103, 9087065421103, 9087060504021103 ... are also in this
sequence and larger that the current a(1).

Maximilian

```