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

1,2

Comments

See A352938 for the other k's.

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

Formula

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

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

Example

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]

Prog

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

Crossrefs

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

Sequence in context: A328472 A046653 A308897 * A162190 A349325 A134292

Adjacent sequences: A353290 A353291 A353292 * A353294 A353295 A353296

Keyword

nonn,tabf,look,base

Author

Rémy Sigrist, Apr 09 2022

Status

approved