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Lexicographically earliest sequence of distinct positive integers such that for any n>0, n and a(n) have no common 1-bit in their binary representations, and no two successive terms have a common 1-bit in their binary representations.
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%I #11 Apr 25 2016 12:00:16

%S 2,1,4,3,8,16,32,5,18,33,20,34,64,17,96,6,40,65,12,35,72,128,104,7,

%T 160,68,256,66,288,129,320,9,22,73,132,10,80,136,272,67,144,69,384,19,

%U 192,257,208,11,196,264,512,74,640,265,576,130,260,193,516,131,768

%N Lexicographically earliest sequence of distinct positive integers such that for any n>0, n and a(n) have no common 1-bit in their binary representations, and no two successive terms have a common 1-bit in their binary representations.

%C This sequence combines the constraints met in A109812 and in A238757.

%C This sequence is a permutation of the positive integers, with inverse A262230.

%H Paul Tek, <a href="/A262155/b262155.txt">Table of n, a(n) for n = 1..100000</a>

%H Paul Tek, <a href="/A262155/a262155.pl.txt">PERL program for this sequence</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e For n=5:

%e - the values 2, 1, 4 and 3 have already been used;

%e - we have the following candidates:

%e +---+--------+-------------+---------------+

%e | z | Binary | Common bits | Common bits |

%e | | digits | with 5 | with a(5-1)=3 |

%e +---+--------+-------------+---------------+

%e | 5 | 101 | 101 | 1 |

%e | 6 | 110 | 100 | 10 |

%e | 7 | 111 | 101 | 11 |

%e | 8 | 1000 | 0 | 0 |

%e |...| ... | ... | ... |

%e +---+--------+-------------+---------------+

%e Hence, a(5)=8.

%o (Perl) See Links section.

%Y Cf. A109812, A238757, A262230.

%K nonn,base

%O 1,1

%A _Paul Tek_, Sep 13 2015