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

0,2

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.

Links

Table of n, a(n) for n=0..57.

Example

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,...
...

Prog

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

Crossrefs

Cf. A047855.

Sequence in context: A345050 A285649 A074956 * A069566 A336314 A066818

Adjacent sequences: A176085 A176086 A176087 * A176089 A176090 A176091

Keyword

nonn,tabl

Author

Rick L. Shepherd, Apr 10 2010

Status

approved