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

1,3

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.

Links

Table of n, a(n) for n=1..52.

Example

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).

Sequence in context: A052018 A352461 A302768 * A180480 A080459 A093475

Adjacent sequences: A202269 A202270 A202271 * A202273 A202274 A202275

Keyword

nonn,base

Author

Jaroslav Krizek, Jan 06 2012

Status

approved