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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.
2

%I #26 Jan 05 2024 13:43:41

%S 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,

%T 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,

%U 14,0,1,4,5,8,9,12,13,0,4,8,12,0,1,2,3,8,9,10,11

%N 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.

%C See A353293 for the other k's.

%H Rémy Sigrist, <a href="/A352938/b352938.txt">Table of n, a(n) for n = 0..9841</a> (rows for n = 0..511 flattened)

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

%F T(n, 1) = 0.

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

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

%e 0: [0]

%e 1: [0]

%e 2: [0, 1]

%e 3: [0]

%e 4: [0, 1, 2, 3]

%e 5: [0, 2]

%e 6: [0, 1]

%e 7: [0]

%e 8: [0, 1, 2, 3, 4, 5, 6, 7]

%e 9: [0, 2, 4, 6]

%e 10: [0, 1, 4, 5]

%e 11: [0, 4]

%e 12: [0, 1, 2, 3]

%e 13: [0, 2]

%e 14: [0, 1]

%e 15: [0]

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

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

%K nonn,tabf,look,base

%O 0,8

%A _Rémy Sigrist_, Apr 09 2022