A352938 Irregular table T(n, k), n >= 0, k = 1..A080100(n), read by rows: the n-th row contains in ascending order the distinct nonnegative integers k <= n that have no common 1-bit with n.

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

Offset

0,8

Comments

See A353293 for the other k's.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..9841 (rows for n = 0..511 flattened)

Index entries for sequences related to binary expansion of n

Formula

T(n, 1) = 0.

T(n, A080100(n)) = A035327(n) for any n > 0.

Example

Irregular table T(n, k) begins:
     0:   [0]
     1:   [0]
     2:   [0, 1]
     3:   [0]
     4:   [0, 1, 2, 3]
     5:   [0, 2]
     6:   [0, 1]
     7:   [0]
     8:   [0, 1, 2, 3, 4, 5, 6, 7]
     9:   [0, 2, 4, 6]
    10:   [0, 1, 4, 5]
    11:   [0, 4]
    12:   [0, 1, 2, 3]
    13:   [0, 2]
    14:   [0, 1]
    15:   [0]

Prog

(PARI) row(n) = select(k -> bitand(n, k)==0, [0..n])

Crossrefs

Cf. A035327, A080100 (row length), A335587 (row sums), A353293.

Sequence in context: A059066 A059067 A356707 * A065861 A329393 A336207

Adjacent sequences: A352935 A352936 A352937 * A352939 A352940 A352941

Keyword

nonn,tabf,look,base

Author

Rémy Sigrist, Apr 09 2022

Status

approved