A179309 The smallest number that has more copies of some digit than any previous number in the sequence.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1000, 1111, 2222, 3333, 4444, 5555, 6666, 7777, 8888, 9999, 10000, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999, 100000

Offset: 1

Author

Jack W Grahl, Jul 10 2010

Keywords

• base
• easy
• nonn

Comments

These are, for each digit d and each natural number k, the smallest positive number in which the digit d appears k (or more) times, in numerical order. They are all numbers with all digits repeated except numbers of the form 10^m.

If we started with 0 the term 10 would be missed and all other terms would be the same.

Examples

			100 is included because no previous term contains two 0's. 111 is included because no previous term contains more than 2 1's. Every number between 101 and 110 inclusive is omitted because each contains at most 2 1's (no more than 11) and at most 1 of any other digit (no more than 2 thru 10).
		

Crossrefs

Supersequence of A014181 and A010785. See also A179310.

Programs

Mathematica

With[{nn=5},Join[Flatten[Table[FromDigits[PadRight[{},i,n]],{i,nn},{n,9}]],10^Range[nn]]]//Sort (* Harvey P. Dale, May 31 2016 *)