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A332013 T(n, k) is the least positive m such that floor(n/m) AND floor(k/m) = 0 (where AND denotes the bitwise AND operator). Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0.

%I A332013 #10 Feb 05 2020 08:59:02
%S A332013 1,1,1,1,2,1,1,1,1,1,1,2,3,2,1,1,1,3,3,1,1,1,2,1,4,1,2,1,1,1,1,1,1,1,
%T A332013 1,1,1,2,3,2,5,2,3,2,1,1,1,3,3,5,5,3,3,1,1,1,2,1,3,3,6,3,3,1,2,1,1,1,
%U A332013 1,1,3,3,3,3,1,1,1,1,1,2,3,2,1,3,7,3,1
%N A332013 T(n, k) is the least positive m such that floor(n/m) AND floor(k/m) = 0 (where AND denotes the bitwise AND operator). Square array T(n, k) read by antidiagonals, n >= 0 and k >= 0.
%C A332013 Sierpinski gasket appears at different scales in the representation of the table (see illustration in Links section).
%H A332013 Rémy Sigrist, <a href="/A332013/b332013.txt">Table of n, a(n) for n = 0..10010</a> (antidiagonals 0..140)
%H A332013 Rémy Sigrist, <a href="/A332013/a332013.png">Colored representation of T(n, k) for n, k = 0..1024</a> (where the hue is function of T(n, k), red pixels correspond to 1's)
%H A332013 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle">Sierpiński triangle</a>
%F A332013 T(n, k) = T(k, n).
%F A332013 T(n, k) = 1 iff n AND k = 0.
%F A332013 T(n, n) = n+1.
%F A332013 T(n, n+1) = A000265(n+1).
%e A332013 Array T(n, k) begins:
%e A332013   n\k|  0  1  2  3  4  5  6  7  8  9 10 11 12
%e A332013   ---+---------------------------------------
%e A332013     0|  1  1  1  1  1  1  1  1  1  1  1  1  1
%e A332013     1|  1  2  1  2  1  2  1  2  1  2  1  2  1
%e A332013     2|  1  1  3  3  1  1  3  3  1  1  3  3  1
%e A332013     3|  1  2  3  4  1  2  3  3  1  2  4  4  1
%e A332013     4|  1  1  1  1  5  5  3  3  1  1  1  1  3
%e A332013     5|  1  2  1  2  5  6  3  3  1  2  1  2  3
%e A332013     6|  1  1  3  3  3  3  7  7  1  1  4  4  3
%e A332013     7|  1  2  3  3  3  3  7  8  1  2  4  4  3
%e A332013     8|  1  1  1  1  1  1  1  1  9  9  5  5  3
%e A332013     9|  1  2  1  2  1  2  1  2  9 10  5  5  3
%e A332013    10|  1  1  3  4  1  1  4  4  5  5 11 11  3
%e A332013    11|  1  2  3  4  1  2  4  4  5  5 11 12  3
%e A332013    12|  1  1  1  1  3  3  3  3  3  3  3  3 13
%o A332013 (PARI) T(n,k) = for (m=1, oo, if (bitand(n\m, k\m)==0, return (m)))
%Y A332013 Cf. A000265, A331886.
%K A332013 nonn,base,tabl
%O A332013 0,5
%A A332013 _Rémy Sigrist_, Feb 04 2020