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A341841 Square array T(n, k), n, k >= 0, read by antidiagonals upwards; for any number m with runs in binary expansion (r_1, ..., r_j), let R(m) = {r_1 + ... + r_j, r_2 + ... + r_j, ..., r_j}; T(n, k) is the unique number t such that R(t) equals R(n) minus R(k). 3
0, 1, 0, 2, 0, 0, 3, 3, 0, 0, 4, 3, 0, 1, 0, 5, 4, 0, 1, 1, 0, 6, 4, 7, 0, 1, 0, 0, 7, 7, 7, 7, 0, 0, 0, 0, 8, 7, 7, 6, 0, 0, 3, 1, 0, 9, 8, 7, 6, 1, 0, 3, 2, 1, 0, 10, 8, 8, 7, 1, 0, 3, 3, 2, 0, 0, 11, 11, 8, 8, 0, 0, 3, 3, 3, 3, 0, 0, 12, 11, 8, 9, 15, 0, 0, 2, 3, 3, 0, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For any m > 0, R(m) contains the partial sums of the m-th row of A227736; by convention, R(0) = {}.

This sequence uses set subtraction, and is related to:

- A003987 which uses set difference,

- A341839 which uses set union,

- A341840 which uses set intersection.

LINKS

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

Rémy Sigrist, Colored representation of the table for n, k < 2^10

Rémy Sigrist, PARI program for A341841

Index entries for sequences related to binary expansion of n

FORMULA

T(n, n) = 0.

T(n, 0) = n.

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

A070939(T(n, k)) <= A070939(n).

A003188(T(n, k)) = A003188(n) - (A003188(n) AND A003188(k)) (where AND denotes the bitwise AND operator).

EXAMPLE

Array T(n, k) begins:

  n\k|   0   1   2   3   4   5   6   7  8  9  10  11  12  13  14  15

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

    0|   0   0   0   0   0   0   0   0  0  0   0   0   0   0   0   0

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

    2|   2   3   0   1   1   0   3   2  2  3   0   1   1   0   3   2

    3|   3   3   0   0   0   0   3   3  3  3   0   0   0   0   3   3

    4|   4   4   7   7   0   0   3   3  3  3   0   0   7   7   4   4

    5|   5   4   7   6   1   0   3   2  2  3   0   1   6   7   4   5

    6|   6   7   7   6   1   0   0   1  1  0   0   1   6   7   7   6

    7|   7   7   7   7   0   0   0   0  0  0   0   0   7   7   7   7

    8|   8   8   8   8  15  15  15  15  0  0   0   0   7   7   7   7

    9|   9   8   8   9  14  15  15  14  1  0   0   1   6   7   7   6

   10|  10  11   8   9  14  15  12  13  2  3   0   1   6   7   4   5

   11|  11  11   8   8  15  15  12  12  3  3   0   0   7   7   4   4

   12|  12  12  15  15  15  15  12  12  3  3   0   0   0   0   3   3

   13|  13  12  15  14  14  15  12  13  2  3   0   1   1   0   3   2

   14|  14  15  15  14  14  15  15  14  1  0   0   1   1   0   0   1

   15|  15  15  15  15  15  15  15  15  0  0   0   0   0   0   0   0

PROG

(PARI) See Links section.

CROSSREFS

Cf. A003188, A003987, A070939, A227736, A341839, A341840.

Sequence in context: A195664 A053202 A188122 * A050186 A334218 A342984

Adjacent sequences:  A341838 A341839 A341840 * A341842 A341843 A341844

KEYWORD

nonn,tabl,base

AUTHOR

Rémy Sigrist, Feb 21 2021

STATUS

approved

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Last modified December 5 06:52 EST 2021. Contains 349543 sequences. (Running on oeis4.)