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A176088
Table T(n,k) = ceiling(10^n/(10^k-1)), n >= 0, k >= 1, read by antidiagonals.
0
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.
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
KEYWORD
nonn,tabl
AUTHOR
Rick L. Shepherd, Apr 10 2010
STATUS
approved