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

Author

Rémy Sigrist, Apr 09 2022

Keywords

• nonn
• tabf
• look
• base

Comments

See A353293 for the other k's.

Examples

			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]
		

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

Crossrefs

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

Programs

PARI

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

Formula

T(n, 1) = 0.

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