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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 (list; table; graph; refs; listen; history; text; internal format)
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: A082272 A107049 A074956 * A069566 A066818 A005730

Adjacent sequences:  A176085 A176086 A176087 * A176089 A176090 A176091

KEYWORD

nonn,tabl

AUTHOR

Rick L. Shepherd, Apr 10 2010

STATUS

approved

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Last modified August 2 04:43 EDT 2014. Contains 245138 sequences.