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A278388 Lexicographically earliest sequence such that (i*2^a(i)) AND (j*2^a(j)) = 0 for any distinct i and j (AND stands for the bitwise AND operator).

%I A278388 #16 Nov 24 2016 09:45:32
%S A278388 0,0,2,2,5,7,10,3,13,14,18,20,24,27,31,10,35,36,41,34,44,48,53,55,60,
%T A278388 64,69,72,77,81,86,15,51,42,61,89,93,95,101,102,108,109,115,119,123,
%U A278388 128,134,136,138,143,145,149,155,160,166,169,175,180,186,190,196
%N A278388 Lexicographically earliest sequence such that (i*2^a(i)) AND (j*2^a(j)) = 0 for any distinct i and j (AND stands for the bitwise AND operator).
%C A278388 By analogy with A275152, this sequence can be obtained by the following algorithm:
%C A278388 - we start with a half-open line of empty squares with coordinates X=0, X=1, X=2, etc.,
%C A278388 - for n=1, 2, 3, ...: we choose the least k such that the polyomino corresponding to n, shifted by k squares to the right, does not overlap one of the previous polyominoes.
%C A278388 a(2*k+1) > a(2*k) for any k>0.
%H A278388 Rémy Sigrist, <a href="/A278388/b278388.txt">Table of n, a(n) for n = 1..10000</a>
%e A278388 The following table depicts the first terms, alongside the corresponding polyominoes ("X" denotes a filled square, "_" denotes an empty square):
%e A278388 n     n in binary    a(n)    n as a polyomino shifted by a(n) to the right
%e A278388 --    -----------    ----    ---------------------------------------------
%e A278388 1     1              0       X
%e A278388 2     10             0       _X
%e A278388 3     11             2         XX
%e A278388 4     100            2         __X
%e A278388 5     101            5            X_X
%e A278388 6     110            7              _XX
%e A278388 7     111            10                XXX
%e A278388 8     1000           3          ___X
%e A278388 9     1001           13                   X__X
%e A278388 10    1010           14                    _X_X
%e A278388 11    1011           18                        XX_X
%e A278388 12    1100           20                          __XX
%e A278388 13    1101           24                              X_XX
%e A278388 14    1110           27                                 _XXX
%e A278388 15    1111           31                                     XXXX
%e A278388 16    10000          10                ____X
%e A278388 17    10001          35                                         X___X
%e A278388 18    10010          36                                          _X__X
%o A278388 (PARI) sumn2a = 0; for (n=1, 1 000, a=0; while (bitand(sumn2a, n<<a), a++); print1 (a ", "); sumn2a += n<<a)
%Y A278388 Cf. A275152.
%K A278388 nonn,base
%O A278388 1,3
%A A278388 _Rémy Sigrist_, Nov 20 2016