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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.

%I A353293 #14 Jan 05 2024 13:43:00
%S A353293 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 A353293 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 A353293 11,12,13,2,3,4,5,6,7,8,9,10,11,12,13,14
%N 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.
%C A353293 See A352938 for the other k's.
%H A353293 Rémy Sigrist, <a href="/A353293/b353293.txt">Table of n, a(n) for n = 1..7163</a> (rows for n = 1..128 flattened)
%H A353293 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A353293 T(n, 1) = A006519(n).
%F A353293 T(n, A353292(n)) = n.
%e A353293 Irregular table T(n, k) begins:
%e A353293      1:   [1]
%e A353293      2:   [2]
%e A353293      3:   [1, 2, 3]
%e A353293      4:   [4]
%e A353293      5:   [1, 3, 4, 5]
%e A353293      6:   [2, 3, 4, 5, 6]
%e A353293      7:   [1, 2, 3, 4, 5, 6, 7]
%e A353293      8:   [8]
%e A353293      9:   [1, 3, 5, 7, 8, 9]
%e A353293     10:   [2, 3, 6, 7, 8, 9, 10]
%e A353293     11:   [1, 2, 3, 5, 6, 7, 8, 9, 10, 11]
%e A353293     12:   [4, 5, 6, 7, 8, 9, 10, 11, 12]
%e A353293     13:   [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
%e A353293     14:   [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
%e A353293     15:   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
%o A353293 (PARI) row(n) = select (k -> bitand(n, k), [1..n])
%Y A353293 Cf. A006519, A352938, A353292 (row lengths).
%K A353293 nonn,tabf,look,base
%O A353293 1,2
%A A353293 _Rémy Sigrist_, Apr 09 2022