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A number is said to be pandigital if it contains each of the digits from 0 to 9 (and whose leading digit must be nonzero). However, "zeroless" pandigital quantities
contain the digits 1 through 9. Sometimes exclusivity is also required so that each
digit is restricted to appear exactly once. For example, 6729/13458 is a (zeroless,
restricted) pandigital fraction
and 1023456789 is the smallest (zerofull) pandigital number.
The first few zerofull restricted pandigital numbers are 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, ... (Sloane's A050278). A 10-digit pandigital number is always divisible
by 9 since
This passes the divisibility test for 9 since  .
The smallest unrestricted pandigital primes must therefore have 11 digits (no two of which can be 0). The first few unrestricted pandigital primes are therefore 10123457689,
10123465789, 10123465897, 10123485679, ... (Sloane's A050288).
If zeros are excluded, the first few "zeroless" restricted pandigital numbers are 123456789, 123456798, 123456879, 123456897, 123456978, 123456987, ... (Sloane's
A050289),
and the first few zeroless pandigital primes are 1123465789, 1123465879, 1123468597,
1123469587, 1123478659, ... (Sloane's A050290).
The sum of the first 32423 (a palindromic number) consecutive primes
is 5897230146, which is restricted pandigital (G.L. Honaker, Jr., pers. comm.).
No other palindromic number
shares this property.
Numbers  that give zeroless pandigital numbers
when the Fibonacci recurrence
with  and  is applied
are 718, 1790, 1993, 2061, 2259, 3888, 3960, 4004, 4396, 5093, 5832, 7031, 7310,
7712, 8039, 8955, 9236, ....
De Geest, P. "The Nine Digits Page." http://www.worldofnumbers.com/ninedigits.htm.
Sloane, N. J. A. Sequences A050278, A050288, A050289, and A050290 in "The On-Line Encyclopedia of Integer Sequences."
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