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A352809 Lexicographically earliest sequence of distinct nonnegative integers such that for any proper divisor d of n the binary expansions of a(d) and a(n) have no common 1's.

%I A352809 #20 Apr 09 2022 13:11:43
%S A352809 0,1,2,4,3,8,5,10,9,12,6,16,7,18,20,32,11,36,13,48,24,40,14,64,28,56,
%T A352809 52,72,15,96,17,80,25,68,88,128,19,34,104,192,21,160,22,144,224,112,
%U A352809 23,256,26,288,84,320,27,384,120,416,176,208,29,512,30,38,352
%N A352809 Lexicographically earliest sequence of distinct nonnegative integers such that for any proper divisor d of n the binary expansions of a(d) and a(n) have no common 1's.
%C A352809 This sequence is a bijection from the positive integers onto the nonnegative integers (with inverse A353266); as a(1) = 0, for any prime number p, a(p) is the least value not yet in the sequence, and eventually every nonnegative integer will appear in the sequence.
%H A352809 Rémy Sigrist, <a href="/A352809/b352809.txt">Table of n, a(n) for n = 1..10000</a>
%H A352809 Rémy Sigrist, <a href="/A352809/a352809.gp.txt">PARI program</a>
%H A352809 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A352809 The first terms, alongside their binary expansion, proper divisors and implied forbidden bits, are:
%e A352809   n   a(n)  bin(a(n))  proper divisors  bin(forbidden)
%e A352809   --  ----  ------     ---------------  --------------
%e A352809    1     0          0  {}                            0
%e A352809    2     1          1  {1}                           0
%e A352809    3     2         10  {1}                           0
%e A352809    4     4        100  {1, 2}                        1
%e A352809    5     3         11  {1}                           0
%e A352809    6     8       1000  {1, 2, 3}                    11
%e A352809    7     5        101  {1}                           0
%e A352809    8    10       1010  {1, 2, 3}                   101
%e A352809    9     9       1001  {1, 2}                       10
%e A352809   10    12       1100  {1, 2, 3}                    11
%e A352809   11     6        110  {1}                           0
%e A352809   12    16      10000  {1, 2, 3, 4, 5}            1111
%e A352809   13     7        111  {1}                           0
%e A352809   14    18      10010  {1, 2, 3}                   101
%o A352809 (PARI) See Links section.
%Y A352809 Cf. A027751, A353266 (inverse).
%K A352809 nonn,base
%O A352809 1,3
%A A352809 _Rémy Sigrist_, Apr 04 2022