A202272 Numbers n with k digits such that each sum of 1, 2, ..., k digits of n is a substring of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 109, 200, 300, 400, 500, 600, 700, 800, 910, 1000, 1009, 1090, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000, 9010, 9100, 10000, 10009, 10090, 10900, 20000, 30000, 40000, 50000, 60000, 70000

Offset: 1

Author

Jaroslav Krizek, Jan 06 2012

Keywords

• nonn
• base

Comments

Conjecture: sequence contains only

- numbers of the form k*10^j (j>=0, k>=0),

- numbers of the form 10X, where X = string of k digits containing one digit 9 and k-1 digits 0 (k>=1),

- numbers of form 9Y10Z; where Y = string of k digits 0 (k>=0), Z = string of j digits 0 (j>=0).

Subsequence of A052018.

Examples

			109 is a term because all possible sums of digits 0, 1, 1, 9, 9, 10 are its substrings.
		

Crossrefs

Cf. A052018 (numbers k such that the sum of the digits of k is substring of k).