[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
this additional restrictions.
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
anything about this issue.
(*) 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
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