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%I #16 Nov 24 2016 09:45:32
%S 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 64,69,72,77,81,86,15,51,42,61,89,93,95,101,102,108,109,115,119,123,
%U 128,134,136,138,143,145,149,155,160,166,169,175,180,186,190,196
%N 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 By analogy with A275152, this sequence can be obtained by the following algorithm:
%C - we start with a half-open line of empty squares with coordinates X=0, X=1, X=2, etc.,
%C - 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 a(2*k+1) > a(2*k) for any k>0.
%H Rémy Sigrist, <a href="/A278388/b278388.txt">Table of n, a(n) for n = 1..10000</a>
%e The following table depicts the first terms, alongside the corresponding polyominoes ("X" denotes a filled square, "_" denotes an empty square):
%e n n in binary a(n) n as a polyomino shifted by a(n) to the right
%e -- ----------- ---- ---------------------------------------------
%e 1 1 0 X
%e 2 10 0 _X
%e 3 11 2 XX
%e 4 100 2 __X
%e 5 101 5 X_X
%e 6 110 7 _XX
%e 7 111 10 XXX
%e 8 1000 3 ___X
%e 9 1001 13 X__X
%e 10 1010 14 _X_X
%e 11 1011 18 XX_X
%e 12 1100 20 __XX
%e 13 1101 24 X_XX
%e 14 1110 27 _XXX
%e 15 1111 31 XXXX
%e 16 10000 10 ____X
%e 17 10001 35 X___X
%e 18 10010 36 _X__X
%o (PARI) sumn2a = 0; for (n=1, 1 000, a=0; while (bitand(sumn2a, n<<a), a++); print1 (a ", "); sumn2a += n<<a)
%Y Cf. A275152.
%K nonn,base
%O 1,3
%A _Rémy Sigrist_, Nov 20 2016