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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. 1

%I #10 Feb 05 2020 08:59:02

%S 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 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 1,1,3,3,3,3,1,1,1,1,1,2,3,2,1,3,7,3,1

%N 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 Sierpinski gasket appears at different scales in the representation of the table (see illustration in Links section).

%H Rémy Sigrist, <a href="/A332013/b332013.txt">Table of n, a(n) for n = 0..10010</a> (antidiagonals 0..140)

%H 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle">Sierpiński triangle</a>

%F T(n, k) = T(k, n).

%F T(n, k) = 1 iff n AND k = 0.

%F T(n, n) = n+1.

%F T(n, n+1) = A000265(n+1).

%e Array T(n, k) begins:

%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12

%e ---+---------------------------------------

%e 0| 1 1 1 1 1 1 1 1 1 1 1 1 1

%e 1| 1 2 1 2 1 2 1 2 1 2 1 2 1

%e 2| 1 1 3 3 1 1 3 3 1 1 3 3 1

%e 3| 1 2 3 4 1 2 3 3 1 2 4 4 1

%e 4| 1 1 1 1 5 5 3 3 1 1 1 1 3

%e 5| 1 2 1 2 5 6 3 3 1 2 1 2 3

%e 6| 1 1 3 3 3 3 7 7 1 1 4 4 3

%e 7| 1 2 3 3 3 3 7 8 1 2 4 4 3

%e 8| 1 1 1 1 1 1 1 1 9 9 5 5 3

%e 9| 1 2 1 2 1 2 1 2 9 10 5 5 3

%e 10| 1 1 3 4 1 1 4 4 5 5 11 11 3

%e 11| 1 2 3 4 1 2 4 4 5 5 11 12 3

%e 12| 1 1 1 1 3 3 3 3 3 3 3 3 13

%o (PARI) T(n,k) = for (m=1, oo, if (bitand(n\m, k\m)==0, return (m)))

%Y Cf. A000265, A331886.

%K nonn,base,tabl

%O 0,5

%A _Rémy Sigrist_, Feb 04 2020

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Last modified March 28 13:35 EDT 2024. Contains 371254 sequences. (Running on oeis4.)