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%I #14 Jul 25 2023 09:51:17
%S 2,2,2,2,3,2,2,2,2,2,2,3,5,3,2,2,2,3,3,2,2,2,4,2,3,2,4,2,2,2,2,2,2,2,
%T 2,2,2,3,3,3,3,3,3,3,2,2,2,5,5,4,4,5,5,2,2,2,3,2,6,4,4,4,6,2,3,2,2,2,
%U 2,2,4,4,4,4,2,2,2,2,2,5,5,3,2,5,5,5,2,3,5,5,2
%N Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the least base >= 2 where the sum n + k can be computed without carry.
%H Rémy Sigrist, <a href="/A362366/b362366.txt">Table of n, a(n) for n = 0..10010</a>
%H Wolfdieter Lang, <a href="https://arxiv.org/abs/2307.10645">Cantor's List of Real Algebraic Numbers of Heights 1 to 7</a>, arXiv:2307.10645 [math.NT], 2023.
%H Rémy Sigrist, <a href="/A362366/a362366.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) = 2.
%F A(n, n) = A321882(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 3 2 3 2 4 2 3 2 3 2 5 2
%e 2 | 2 2 5 3 2 2 3 5 2 2 5 5 2
%e 3 | 2 3 3 3 2 3 5 6 2 3 3 3 2
%e 4 | 2 2 2 2 3 4 4 4 2 2 2 2 3
%e 5 | 2 4 2 3 4 4 4 5 2 3 2 5 3
%e 6 | 2 2 3 5 4 4 5 5 2 2 3 3 5
%e 7 | 2 3 5 6 4 5 5 5 2 3 3 5 5
%e 8 | 2 2 2 2 2 2 2 2 6 3 5 5 6
%e 9 | 2 3 2 3 2 3 2 3 3 3 3 3 3
%e 10 | 2 2 5 3 2 2 3 3 5 3 3 5 3
%e 11 | 2 5 5 3 2 5 3 5 5 3 5 5 3
%e 12 | 2 2 2 2 3 3 5 5 6 3 3 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. A321882, A362367.
%K nonn,base,tabl
%O 0,1
%A _Rémy Sigrist_, Apr 17 2023
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