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pandigital numbers
A number  $n$  is pandigital in base  $b$  if its base  $b$  representation contains all the possible digits, i.e., 0, 1, ..., b-1, at least once.

If  $n$  contain each digit exactly once, it is called strictly pandigital.

For example, 1023456789 is the smallest (strictly) pandigital number in base 10, while  $270=(10032)_4$  is pandigital in base 4 but not strictly pandigital.

Many authors use simply the term pandigital to mean both kind of numbers, so I will do the same, since usually the right meaning will be clear from the contest.

The first strictly pandigital numbers, in any possible base  $b\ge2$  are 2, 11, 15, 19, 21, 75, 78, 99, 108, 114, 120, 135, 141, 147, 156, 177, 180, 198, 201, 210, 216, 225, 228, 694, 698, 714, 722, 738, 742, 894 more terms

Pandigitals can also be... (you may click on names or numbers and on + to get more values)

a-pointer 11 ABA 722 1922 6002500 + 9743521608 aban 11 15 19 + 380000948 abundant 78 108 114 + 47754948 Achilles 108 128547 254043 + 9876523104 admirable 78 114 120 + 95510716 alt.fact. 19 alternating 21 78 141 + 298989892 amenable 21 108 120 + 381367044 amicable 1210 124155 525915 + 5209468173 apocalyptic 714 894 898 + 29965 arithmetic 11 15 19 + 9998170 astonishing 15 216 Bell 15 betrothed 75 2573840619 binomial 15 21 78 + 9654871320 brilliant 15 21 c.decagonal 11 c.heptagonal 94986116 104550916 108762676 + 229946956 c.nonagonal 2926 23005 29890 + 339861556 c.octagonal 225 38025 314721 + 9614783025 c.pentagonal 141 69129556 91279516 + 380103076 c.square 21425 27145 42925 c.triangular 19 694 1054 + 377047756 cake 15 383439 Chen 11 19 congruent 15 21 78 + 9998037 constructible 15 120 20560 30720 cube 216 Cunningham 15 99 120 + 9743861520 Curzon 21 78 114 + 16434369 cyclic 11 15 19 + 9997981 D-number 15 21 141 + 799899 d-powerful 135 1634 2134 + 9977513 de Polignac 16405 17735 23935 + 16433683 decagonal 742 22275 124785 + 9576432810 deficient 11 15 19 + 9998163 dig.balanced 11 15 19 + 199999932 double fact. 15 Duffinian 21 75 201 + 9998163 eban 2054 30040 30050 + 66060044 economical 11 15 19 + 16434817 emirpimes 15 177 1202 + 16421923 equidigital 11 15 19 + 16434817 eRAP 709929 89271996 185164700 + 8460391257 esthetic 21 78 210 + 9876543210 Eulerian 11 120 evil 15 75 78 + 381367044 factorial 120 fibodiv 19 75 32525 + 1042765893 Fibonacci 21 Friedman 216 1022 10575 + 781263 frugal 11045 12125 21870 + 379233148 gapful 108 120 135 + 9876543210 Gilda 78 990 good prime 11 happy 19 694 970 + 9998037 harmonic 2178540 Harshad 21 108 114 + 9876543210 heptagonal 970 785961 2207590 + 9386472150 hex 19 2252467 3124261 + 13337317 hexagonal 15 120 8385 + 9654871320 highly composite 120 180 hoax 2826 2902 8415 + 95581084 Hogben 21 217623 228963 + 15401701 house 78 13600909 hyperperfect 21 iban 11 21 114 + 774411 idoneal 15 21 78 + 210 inconsummate 75 216 1646 + 800661 interprime 15 21 99 + 95583996 Jacobsthal 11 21 699051 Jordan-Polya 120 216 30720 junction 210 216 1014 + 95584540 Kaprekar 99 5479453 katadrome 21 75 210 + 9876543210 Lehmer 15 16405 39865 + 14821261 Leyland 177 lonely 120 Lucas 11 lucky 15 21 75 + 9998163 Lynch-Bell 15 135 216 3817296 magic 15 210975 magnanimous 11 21 970 + 42265 metadrome 15 19 78 + 124689 modest 19 1022 2022 + 1980467532 Moran 21 114 156 + 95454108 Motzkin 21 41835 narcissistic 1634 nialpdrome 11 21 75 + 9876543210 nonagonal 75 170391 598851 + 9762483051 nude 11 15 99 + 379772316 O'Halloran 156 oban 11 15 19 + 990 octagonal 21 225 12545 + 9053782416 odious 11 19 21 + 381366972 palindromic 11 99 141 + 298989892 palprime 11 pancake 11 742 1654 + 341270876 panconsummate 11 15 21 78 partition 11 15 135 239943 pentagonal 210 2882 16485 + 9120345876 pernicious 11 19 21 + 800661 persistent 1023456789 1023456879 1023457689 + 9876543210 Pierpont 19 plaindrome 11 15 19 + 334466788 Poulet 39865 212421 5258701 + 8137633 power 216 225 38025 + 9814072356 powerful 108 216 225 + 9876523104 practical 78 108 120 + 9998058 prim.abundant 78 114 894 + 95510716 prime 11 19 primorial 210 pronic 156 210 1190 + 9854632170 Proth 177 225 11265 + 8736210945 pseudoperfect 78 108 114 + 797895 repdigit 11 99 repfigit 19 75 742 repunit 15 21 156 + 15401701 Rhonda 13521354 Ruth-Aaron 15 78 714 + 9723805461 Saint-Exupery 20580 30720 33600 + 8439576120 self 75 108 198 + 381366956 semiprime 15 21 141 + 16434817 sliding 11 16265 200432500 Smith 2902 9015 19615 + 95580940 sphenic 78 114 742 + 16434201 square 225 38025 314721 + 9814072356 straight-line 135 147 210 + 9876543210 strobogrammatic 11 88669988 91196116 strong prime 11 super Niven 120 210 990 + 360033300 super-d 19 1054 1070 + 9998058 superabundant 120 180 tau 108 156 180 + 381367044 taxicab 11548089 1430867592 3928157064 + 9083647125 tetrahedral 120 37820 43680 + 131908700 tetranacci 15 108 1490 triangular 15 21 78 + 9654871320 trimorphic 75 99 twin 11 19 uban 11 15 19 + 69000020 Ulam 11 99 114 + 9998037 undulating 141 898 8585 + 434343 unprimeable 894 898 1070 + 9998058 untouchable 120 210 216 + 44760 upside-down 19 2558 124689 + 282951828 vampire 15249780 80993700 81739588 + 8210953476 wasteful 75 78 99 + 9998170 weak prime 19 weird 10570 13790 26110 30170 Wieferich 298389 Zeisel 25085 Zuckerman 11 15 135 + 13226976 Zumkeller 78 108 114 + 44790 zygodrome 11 99 33555 + 339955500