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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
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, 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, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 2, 3, 2, 1, 3, 7, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10010 (antidiagonals 0..140)

Rémy Sigrist, Colored representation of T(n, k) for n, k = 0..1024 (where the hue is function of T(n, k), red pixels correspond to 1's)

Wikipedia, Sierpiński triangle

FORMULA

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

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

T(n, n) = n+1.

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

EXAMPLE

Array T(n, k) begins:

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

  ---+---------------------------------------

    0|  1  1  1  1  1  1  1  1  1  1  1  1  1

    1|  1  2  1  2  1  2  1  2  1  2  1  2  1

    2|  1  1  3  3  1  1  3  3  1  1  3  3  1

    3|  1  2  3  4  1  2  3  3  1  2  4  4  1

    4|  1  1  1  1  5  5  3  3  1  1  1  1  3

    5|  1  2  1  2  5  6  3  3  1  2  1  2  3

    6|  1  1  3  3  3  3  7  7  1  1  4  4  3

    7|  1  2  3  3  3  3  7  8  1  2  4  4  3

    8|  1  1  1  1  1  1  1  1  9  9  5  5  3

    9|  1  2  1  2  1  2  1  2  9 10  5  5  3

   10|  1  1  3  4  1  1  4  4  5  5 11 11  3

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

   12|  1  1  1  1  3  3  3  3  3  3  3  3 13

PROG

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

CROSSREFS

Cf. A000265, A331886.

Sequence in context: A287957 A003989 A091255 * A324350 A175466 A214403

Adjacent sequences:  A332010 A332011 A332012 * A332014 A332015 A332016

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, Feb 04 2020

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)