Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Apr 20 2023 14:44:11
%S 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,
%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,3,2,2,2,2,2,2,3,2,4,2,3,2,2,2,2,2,
%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,5,5,5,2,2,2,2,2
%N Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the least base >= 2 where the product n * k can be computed without carry.
%H Rémy Sigrist, <a href="/A362367/b362367.txt">Table of n, a(n) for n = 0..10010</a>
%H Rémy Sigrist, <a href="/A362367/a362367.png">Colored representation of the array for n, k <= 1024</a> (the color is function of A(n, k), black pixels denote 2's)
%F A(n, k) <= max(2, n*k + 1).
%F A(n, k) = A(k, n).
%F A(n, 0) = A(n, 1) = A(n, 2) = 2.
%F A(n, n) = A319478(n).
%e Array A(n, k) begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12
%e ----+-----------------------------------------
%e 0 | 2 2 2 2 2 2 2 2 2 2 2 2 2
%e 1 | 2 2 2 2 2 2 2 2 2 2 2 2 2
%e 2 | 2 2 2 2 2 2 2 2 2 2 2 2 2
%e 3 | 2 2 2 3 2 2 3 3 2 2 2 3 3
%e 4 | 2 2 2 2 2 2 2 2 2 2 2 2 2
%e 5 | 2 2 2 2 2 4 2 5 2 2 3 5 2
%e 6 | 2 2 2 3 2 2 5 5 2 2 2 5 3
%e 7 | 2 2 2 3 2 5 5 5 2 2 3 7 6
%e 8 | 2 2 2 2 2 2 2 2 2 2 2 2 2
%e 9 | 2 2 2 2 2 2 2 2 2 3 2 3 2
%e 10 | 2 2 2 2 2 3 2 3 2 2 3 5 2
%e 11 | 2 2 2 3 2 5 5 7 2 3 5 5 3
%e 12 | 2 2 2 3 2 2 3 6 2 2 2 3 3
%o (PARI) A(n, k) = { for (b = 2, oo, if (sumdigits(n*k, b) == sumdigits(n, b) * sumdigits(k, b), return (b););); }
%Y Cf. A319478, A362366.
%K nonn,base,tabl
%O 0,1
%A _Rémy Sigrist_, Apr 17 2023