A353293 Irregular table T(n, k), n > 0, k = 1..A353292(n), read by rows: the n-th row contains in ascending order the distinct positive integers k <= n that have at least one common 1-bit with n.

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

Offset: 1

Author

Rémy Sigrist, Apr 09 2022

Keywords

• nonn
• tabf
• look
• base

Comments

See A352938 for the other k's.

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..7163 (rows for n = 1..128 flattened)
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A006519, A352938, A353292 (row lengths).

Programs

PARI

row(n) = select (k -> bitand(n, k), [1..n])

Formula

T(n, 1) = A006519(n).

T(n, A353292(n)) = n.