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%I #14 Mar 27 2018 16:27:15
%S 0,0,1,0,1,2,0,1,2,3,0,1,2,3,4,0,1,2,3,4,5,0,1,2,3,4,5,6,0,1,2,3,4,5,
%T 6,7,0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,9,0,10,10,10,10,10,10,10,10,
%U 10,10,0,1,20,11,11,11,11,11,11,11,11,11,0,1
%N Square array T(n, k), n >= 0, k >= 0, read by antidiagonals upwards: T(n, k) = the (k+1)-th nonnegative number m such that n + m can be computed with carry in decimal base.
%C The corresponding sequence for the binary base is A295653.
%H Rémy Sigrist, <a href="/A298486/b298486.txt">Table of n, a(n) for n = 0..5150</a>
%F For any n >= 0 and k >= 0:
%F - T(0, k) = k,
%F - T(9, k) = 10 * k,
%F - T(10^n - 1, k) = 10^n * k,
%F - T(n, 0) = 0,
%F - T(n, 1) = 10^A122840(n+1),
%F - T(n, k + A298372(n)) = k + 10^A004218(n+1) (i.e. each row is linear).
%e Square array begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 ...
%e ---+-------------------------------------------------
%e 0| 0 1 2 3 4 5 6 7 8 9 10 ... <-- A001477
%e 1| 0 1 2 3 4 5 6 7 8 10 11 ...
%e 2| 0 1 2 3 4 5 6 7 10 11 12 ...
%e 3| 0 1 2 3 4 5 6 10 11 12 13 ...
%e 4| 0 1 2 3 4 5 10 11 12 13 14 ...
%e 5| 0 1 2 3 4 10 11 12 13 14 20 ...
%e 6| 0 1 2 3 10 11 12 13 20 21 22 ...
%e 7| 0 1 2 10 11 12 20 21 22 30 31 ...
%e 8| 0 1 10 11 20 21 30 31 40 41 50 ...
%e 9| 0 10 20 30 40 50 60 70 80 90 100 ... <-- A008592
%e 10| 0 1 2 3 4 5 6 7 8 9 10 ...
%o (PARI) T(n,k,{base=10}) = my (v=0, p=1); while (k, my (r=base - (n%base)); v += p*(k%r); n \= base; k \= r; p *= base); v
%Y Cf. A001477, A004218, A008592, A122840, A295653, A298372.
%K nonn,base,tabl
%O 0,6
%A _Rémy Sigrist_, Jan 20 2018
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