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A361674 Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.

%I A361674 #11 Mar 21 2023 15:03:39
%S A361674 0,1,2,2,3,4,5,5,5,6,4,5,6,7,8,9,10,11,9,10,10,10,11,10,11,12,13,10,
%T A361674 13,9,10,13,14,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,17,18,21,
%U A361674 22,18,21,18,19,20,21,20,21,21,21,22,20,21,22,23,20,21,22,23,24,25,26,27
%N A361674 Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.
%C A361674 In other words, the n-th row contains the numbers k with the same binary length as n and for any i >= 0, if the i-th bit and the (i+1)-th bit in n are different then they are also different in k (i = 0 corresponding to the least significant bit).
%H A361674 Rémy Sigrist, <a href="/A361674/b361674.txt">Table of n, a(n) for n = 0..9841</a> (rows for n = 0..511 flattened)
%F A361674 T(n, 1) = A361645(n).
%F A361674 T(n, 2^A092339(n)) = A361676(n).
%e A361674 Triangle T(n, k) begins (in decimal and in binary):
%e A361674   n   n-th row        bin(n)  n-th row in binary
%e A361674   --  --------------  ------  ----------------------
%e A361674    0  0                    0  0
%e A361674    1  1                    1  1
%e A361674    2  2                   10  10
%e A361674    3  2, 3                11  10, 11
%e A361674    4  4, 5               100  100, 101
%e A361674    5  5                  101  101
%e A361674    6  5, 6               110  101, 110
%e A361674    7  4, 5, 6, 7         111  100, 101, 110, 111
%e A361674    8  8, 9, 10, 11      1000  1000, 1001, 1010, 1011
%e A361674    9  9, 10             1001  1001, 1010
%e A361674   10  10                1010  1010
%e A361674   11  10, 11            1011  1010, 1011
%e A361674   12  10, 11, 12, 13    1100  1010, 1011, 1100, 1101
%e A361674   13  10, 13            1101  1010, 1101
%e A361674   14  9, 10, 13, 14     1110  1001, 1010, 1101, 1110
%o A361674 (PARI) row(n) = { my (r = [n], m); for (e = 1, exponent(n), if (bittest(n, e-1)==bittest(n, e), m = 2^e-1; r = concat(r, [bitxor(v, m) | v <- r]););); vecsort(r); }
%Y A361674 Cf. A361644, A361645, A361676.
%K A361674 nonn,base,tabf
%O A361674 0,3
%A A361674 _Rémy Sigrist_, Mar 20 2023