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A359806 Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2^k) / n) AND floor((2^k) / a(n)) = 0 (where AND denotes the bitwise AND operator).

%I A359806 #6 Jan 14 2023 08:46:12
%S A359806 2,1,6,5,4,3,14,9,8,40,32,24,60,7,20,17,16,144,128,15,72,64,512,12,
%T A359806 256,120,13824,39,2048,35,62,11,1056,544,30,288,4096,1008,28,10,1024,
%U A359806 156,5504,1408,112,1424,8192,96,1016,51200,102,240,32768,27648,248,78
%N A359806 Lexicographically earliest sequence of distinct positive terms such that for any n > 0 and any k > 0, floor((2^k) / n) AND floor((2^k) / a(n)) = 0 (where AND denotes the bitwise AND operator).
%C A359806 In other words, for any n > 0, the binary expansions of 1/n and of 1/a(n) have no common one bit; in this sense, this sequence is similar to A238757.
%C A359806 This sequence is a self-inverse permutation of the positive integers.
%H A359806 Rémy Sigrist, <a href="/A359806/a359806.txt">C++ program</a>
%H A359806 Rémy Sigrist, <a href="/A359806/a359806.gp.txt">PARI program</a>
%H A359806 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A359806 The first terms, alongside the binary expansions of 1/n and 1/a(n) (with periodic parts in parentheses), are:
%e A359806   n   a(n)  bin(1/n)        bin(1/a(n))
%e A359806   --  ----  --------------  -----------
%e A359806    1     2  1.(0)           0.1(0)
%e A359806    2     1  0.1(0)          1.(0)
%e A359806    3     6  0.(01)          0.0(01)
%e A359806    4     5  0.01(0)         0.(0011)
%e A359806    5     4  0.(0011)        0.01(0)
%e A359806    6     3  0.0(01)         0.(01)
%e A359806    7    14  0.(001)         0.0(001)
%e A359806    8     9  0.001(0)        0.(000111)
%e A359806    9     8  0.(000111)      0.001(0)
%e A359806   10    40  0.0(0011)       0.000(0011)
%e A359806   11    32  0.(0001011101)  0.00001(0)
%e A359806   12    24  0.00(01)        0.000(01)
%o A359806 (C++) See Links section.
%o A359806 (PARI) See Links section.
%Y A359806 See A306231 for a similar sequence.
%Y A359806 Cf. A238757.
%K A359806 nonn,base
%O A359806 1,1
%A A359806 _Rémy Sigrist_, Jan 13 2023