A353293 - OEIS

%I #14 Jan 05 2024 13:43:00

%S 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,

%T 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,

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

%N 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.

%C See A352938 for the other k's.

%H Rémy Sigrist, <a href="/A353293/b353293.txt">Table of n, a(n) for n = 1..7163</a> (rows for n = 1..128 flattened)

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

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

%e Irregular table T(n, k) begins:

%e      1:   [1]

%e      2:   [2]

%e      3:   [1, 2, 3]

%e      4:   [4]

%e      5:   [1, 3, 4, 5]

%e      6:   [2, 3, 4, 5, 6]

%e      7:   [1, 2, 3, 4, 5, 6, 7]

%e      8:   [8]

%e      9:   [1, 3, 5, 7, 8, 9]

%e     10:   [2, 3, 6, 7, 8, 9, 10]

%e     11:   [1, 2, 3, 5, 6, 7, 8, 9, 10, 11]

%e     12:   [4, 5, 6, 7, 8, 9, 10, 11, 12]

%e     13:   [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]

%e     14:   [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]

%e     15:   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]

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

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

%K nonn,tabf,look,base

%O 1,2

%A _Rémy Sigrist_, Apr 09 2022