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A262155 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.

%I A262155 #11 Apr 25 2016 12:00:16
%S A262155 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 A262155 160,68,256,66,288,129,320,9,22,73,132,10,80,136,272,67,144,69,384,19,
%U A262155 192,257,208,11,196,264,512,74,640,265,576,130,260,193,516,131,768
%N A262155 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 A262155 This sequence combines the constraints met in A109812 and in A238757.
%C A262155 This sequence is a permutation of the positive integers, with inverse A262230.
%H A262155 Paul Tek, <a href="/A262155/b262155.txt">Table of n, a(n) for n = 1..100000</a>
%H A262155 Paul Tek, <a href="/A262155/a262155.pl.txt">PERL program for this sequence</a>
%H A262155 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A262155 For n=5:
%e A262155 - the values 2, 1, 4 and 3 have already been used;
%e A262155 - we have the following candidates:
%e A262155 +---+--------+-------------+---------------+
%e A262155 | z | Binary | Common bits |  Common bits  |
%e A262155 |   | digits |   with 5    | with a(5-1)=3 |
%e A262155 +---+--------+-------------+---------------+
%e A262155 | 5 |    101 |         101 |             1 |
%e A262155 | 6 |    110 |         100 |            10 |
%e A262155 | 7 |    111 |         101 |            11 |
%e A262155 | 8 |   1000 |           0 |             0 |
%e A262155 |...|    ... |         ... |           ... |
%e A262155 +---+--------+-------------+---------------+
%e A262155 Hence, a(5)=8.
%o A262155 (Perl) See Links section.
%Y A262155 Cf. A109812, A238757, A262230.
%K A262155 nonn,base
%O A262155 1,1
%A A262155 _Paul Tek_, Sep 13 2015