A061845 Numbers that have one of every digit in some base.

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, 898, 954, 970, 978, 990, 1014, 1022, 1054, 1070, 1102, 1110, 1138, 1142, 1178, 1190, 1202, 1210, 1294, 1298, 1334

Offset: 2

Author

Erich Friedman, Jun 23 2001

Keywords

• base
• easy
• nice
• nonn
• tabf

Comments

Also known as pandigital numbers, especially in base 10.

Examples

			Base 3 values are 102_3 = 11, 120_3 = 15, 201_3 = 19, 210_3 = 21.
Triangle begins:
    2;
   11,  15,  19,  21;
   75,  78,  99, 108, 114, 120, 135, 141, 147, 156, 177, 180,  198,  201, ...
  694, 698, 714, 722, 738, 742, 894, 898, 954, 970, 978, 990, 1014, 1022, ...
  ...
		

Links

• Alois P. Heinz, Rows n = 2..8, flattened

Crossrefs

Column k=1 gives A049363 (for n>1).

Last elements of rows give A062813.

Cf. A050278, A134640, A001563 (row lengths).

Programs

Mathematica

dtn[ L_, base_ ] := Fold[ base*#1+#2&, 0, L ] f[ n_ ] := Map[ dtn[ #, n ]&, Select[ Permutations[ Range[ 0, n-1 ] ], First[ # ]>0& ] ] Flatten[ Join[ Table[ f[ i ], {i, 2, 5} ] ] ]