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A375115 Lexicographically earliest sequence of positive integers such that the pairs (a(n) AND a(n+1), a(n+1)) are all distinct (where AND denotes the bitwise AND operator).

%I A375115 #10 Aug 04 2024 12:42:49
%S A375115 0,0,1,1,2,2,3,3,4,3,5,3,6,4,5,5,6,6,7,7,8,5,7,9,6,9,7,10,7,11,7,12,7,
%T A375115 13,8,7,14,9,9,10,10,11,11,12,11,13,11,14,12,13,13,14,14,15,15,16,10,
%U A375115 13,15,17,11,15,18,11,19,12,15,20,11,20,13,18,13,19
%N A375115 Lexicographically earliest sequence of positive integers such that the pairs (a(n) AND a(n+1), a(n+1)) are all distinct (where AND denotes the bitwise AND operator).
%C A375115 The value 0 appears twice; for any v > 0, the value v appears A001316(v) times.
%H A375115 Rémy Sigrist, <a href="/A375115/b375115.txt">Table of n, a(n) for n = 0..10000</a>
%H A375115 Rémy Sigrist, <a href="/A375115/a375115.gp.txt">PARI program</a>
%e A375115 The first terms, alongside the corresponding pairs, are:
%e A375115   n   a(n)  (a(n) AND a(n+1), a(n+1))
%e A375115   --  ----  -------------------------
%e A375115    0     0  (0, 0)
%e A375115    1     0  (0, 1)
%e A375115    2     1  (1, 1)
%e A375115    3     1  (0, 2)
%e A375115    4     2  (2, 2)
%e A375115    5     2  (2, 3)
%e A375115    6     3  (3, 3)
%e A375115    7     3  (0, 4)
%e A375115    8     4  (0, 3)
%e A375115    9     3  (1, 5)
%e A375115   10     5  (1, 3)
%e A375115   11     3  (2, 6)
%e A375115   12     6  (4, 4)
%e A375115   13     4  (4, 5)
%e A375115   14     5  (5, 5)
%e A375115   15     5  (4, 6)
%o A375115 (PARI) \\ See Links section.
%Y A375115 See A375110 for similar sequences.
%Y A375115 Cf. A001316.
%K A375115 nonn,base
%O A375115 0,5
%A A375115 _Rémy Sigrist_, Jul 30 2024