A176088 Table T(n,k) = ceiling(10^n/(10^k-1)), n >= 0, k >= 1, read by antidiagonals.

1, 2, 1, 12, 1, 1, 112, 2, 1, 1, 1112, 11, 1, 1, 1, 11112, 102, 2, 1, 1, 1, 111112, 1011, 11, 1, 1, 1, 1, 1111112, 10102, 101, 2, 1, 1, 1, 1, 11111112, 101011, 1002, 11, 1, 1, 1, 1, 1, 111111112, 1010102, 10011, 101, 2, 1, 1, 1, 1, 1, 1111111112, 10101011, 100101

Offset: 0

Author

Rick L. Shepherd, Apr 10 2010

Keywords

• nonn
• tabl

Comments

For n+1 >= k, minimal number of k-digit base 10 numbers totaling an (n+1)-digit sum.

Column 1 of the table, T(n,1) = 1, 2, 12, 112, 1112, ..., is A047855.

T(n,k) = 1 for k >= n+1.

T(i,i) = 2 for i > 0. Generally, for all m >= 1 and i >= 0, T(2m-1+i,m+i) = 10^(m-1) + 1.

Examples

			The table begins:
.........1,........1,.......1,......1,.....1,....1,...1,..1,.1,1,1,1,...
.........2,........1,.......1,......1,.....1,....1,...1,..1,.1,1,1,1,...
........12,........2,.......1,......1,.....1,....1,...1,..1,.1,1,1,1,...
.......112,.......11,.......2,......1,.....1,....1,...1,..1,.1,1,1,1,...
......1112,......102,......11,......2,.....1,....1,...1,..1,.1,1,1,1,...
.....11112,.....1011,.....101,.....11,.....2,....1,...1,..1,.1,1,1,1,...
....111112,....10102,....1002,....101,....11,....2,...1,..1,.1,1,1,1,...
...1111112,...101011,...10011,...1001,...101,...11,...2,..1,.1,1,1,1,...
..11111112,..1010102,..100101,..10002,..1001,..101,..11,..2,.1,1,1,1,...
.111111112,.10101011,.1001002,.100011,.10001,.1001,.101,.11,.2,1,1,1,...
1111111112,101010102,10010011,1000101,100002,10001,1001,101,11,2,1,1,...
...
		

Crossrefs

Cf. A047855.

Programs

PARI

T(n,k) = if(n>=0 && k>=1, ceil(10^n/(10^k-1)))