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.
A number of interesting pandigital pi approximations are known.
The first few zerofull restricted pandigital numbers are 1023456789, 1023456798, 1023456879, 1023456897, 1023456978, ... (OEIS A050278). A 10-digit pandigital number is always divisible by 9 since
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(1)
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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, ... (OEIS A050288).
If zeros are excluded, the first few "zeroless" restricted pandigital numbers are 123456789, 123456798, 123456879, 123456897, 123456978, 123456987, ... (OEIS A050289), and the first few zeroless pandigital primes are 1123465789, 1123465879, 1123468597, 1123469587, 1123478659, ... (OEIS 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
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(2)
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with 
and 
is applied are 718, 1790, 1993, 2061, 2259, 3888, 3960, 4004, 4396, 5093, 5832, 7031,
7310, 7712, 8039, 8955, 9236, ....
An interesting integer relation exists between the two following fractions of pandigital numbers
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(3)
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(A. Povolotsky, pers. comm., Aug. 27, 2022).
