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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). 1
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, 64, 69, 72, 77, 81, 86, 15, 51, 42, 61, 89, 93, 95, 101, 102, 108, 109, 115, 119, 123, 128, 134, 136, 138, 143, 145, 149, 155, 160, 166, 169, 175, 180, 186, 190, 196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

By analogy with A275152, this sequence can be obtained by the following algorithm:

- we start with a half-open line of empty squares with coordinates X=0, X=1, X=2, etc.,

- 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.

a(2*k+1) > a(2*k) for any k>0.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

EXAMPLE

The following table depicts the first terms, alongside the corresponding polyominoes ("X" denotes a filled square, "_" denotes an empty square):

n     n in binary    a(n)    n as a polyomino shifted by a(n) to the right

--    -----------    ----    ---------------------------------------------

1     1              0       X

2     10             0       _X

3     11             2         XX

4     100            2         __X

5     101            5            X_X

6     110            7              _XX

7     111            10                XXX

8     1000           3          ___X

9     1001           13                   X__X

10    1010           14                    _X_X

11    1011           18                        XX_X

12    1100           20                          __XX

13    1101           24                              X_XX

14    1110           27                                 _XXX

15    1111           31                                     XXXX

16    10000          10                ____X

17    10001          35                                         X___X

18    10010          36                                          _X__X

PROG

(PARI) sumn2a = 0; for (n=1, 1 000, a=0; while (bitand(sumn2a, n<<a), a++); print1 (a ", "); sumn2a += n<<a)

CROSSREFS

Cf. A275152.

Sequence in context: A188623 A256358 A241761 * A239737 A262883 A259446

Adjacent sequences:  A278385 A278386 A278387 * A278389 A278390 A278391

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Nov 20 2016

STATUS

approved

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Last modified February 21 16:28 EST 2018. Contains 299414 sequences. (Running on oeis4.)