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

%I A176088 #2 Mar 30 2012 17:36:45
%S A176088 1,2,1,12,1,1,112,2,1,1,1112,11,1,1,1,11112,102,2,1,1,1,111112,1011,
%T A176088 11,1,1,1,1,1111112,10102,101,2,1,1,1,1,11111112,101011,1002,11,1,1,1,
%U A176088 1,1,111111112,1010102,10011,101,2,1,1,1,1,1,1111111112,10101011,100101
%N A176088 Table T(n,k) = ceiling(10^n/(10^k-1)), n >= 0, k >= 1, read by antidiagonals.
%C A176088 For n+1 >= k, minimal number of k-digit base 10 numbers totaling an (n+1)-digit sum.
%C A176088 Column 1 of the table, T(n,1) = 1, 2, 12, 112, 1112, ..., is A047855.
%C A176088 T(n,k) = 1 for k >= n+1.
%C A176088 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.
%e A176088 The table begins:
%e A176088 .........1,........1,.......1,......1,.....1,....1,...1,..1,.1,1,1,1,...
%e A176088 .........2,........1,.......1,......1,.....1,....1,...1,..1,.1,1,1,1,...
%e A176088 ........12,........2,.......1,......1,.....1,....1,...1,..1,.1,1,1,1,...
%e A176088 .......112,.......11,.......2,......1,.....1,....1,...1,..1,.1,1,1,1,...
%e A176088 ......1112,......102,......11,......2,.....1,....1,...1,..1,.1,1,1,1,...
%e A176088 .....11112,.....1011,.....101,.....11,.....2,....1,...1,..1,.1,1,1,1,...
%e A176088 ....111112,....10102,....1002,....101,....11,....2,...1,..1,.1,1,1,1,...
%e A176088 ...1111112,...101011,...10011,...1001,...101,...11,...2,..1,.1,1,1,1,...
%e A176088 ..11111112,..1010102,..100101,..10002,..1001,..101,..11,..2,.1,1,1,1,...
%e A176088 .111111112,.10101011,.1001002,.100011,.10001,.1001,.101,.11,.2,1,1,1,...
%e A176088 1111111112,101010102,10010011,1000101,100002,10001,1001,101,11,2,1,1,...
%e A176088 ...
%o A176088 (PARI) T(n,k) = if(n>=0 && k>=1, ceil(10^n/(10^k-1)))
%Y A176088 Cf. A047855.
%K A176088 nonn,tabl
%O A176088 0,2
%A A176088 _Rick L. Shepherd_, Apr 10 2010