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%I #13 Mar 03 2024 14:13:17
%S 0,1,2,3,4,5,7,8,6,9,11,15,16,10,14,17,12,13,18,19,23,31,32,20,21,29,
%T 34,24,25,27,36,26,30,33,22,40,41,43,47,63,64,28,35,39,55,72,37,45,61,
%U 66,44,46,62,65,38,54,73,48,49,51,59,68,42,58,69,50,76,77
%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, a(n) AND a(n+1) equals 0 or a(n) (where AND denotes the bitwise AND operator).
%C This sequence is a permutation of the nonnegative integers (with inverse A370794):- we can always extend the sequence with a power of 2 greater than any prior term,
%C - for any k >= 0, the first term >= 2^k is precisely 2^k,
%C - every power of 2 appears in the sequence, in ascending order,
%C - if a(n) = 2^k and the least value not in the sequence at this point, say v, satisfies v < 2^k, then a(n+1) = v, and eventually every nonnegative integer will appear in the sequence.
%H Rémy Sigrist, <a href="/A370793/b370793.txt">Table of n, a(n) for n = 0..10000</a>
%H Rémy Sigrist, <a href="/A370793/a370793.png">Scatterplot of the first 500000 terms</a>
%H Rémy Sigrist, <a href="/A370793/a370793.txt">C++ program</a>
%H Rémy Sigrist, <a href="/A370793/a370793_1.txt">C++ program (faster)</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, alongside the bitwise AND of consecutive terms, are:
%e n a(n) a(n) AND a(n+1)
%e -- ---- ---------------
%e 0 0 0
%e 1 1 0
%e 2 2 2
%e 3 3 0
%e 4 4 4
%e 5 5 5
%e 6 7 0
%e 7 8 0
%e 8 6 0
%e 9 9 9
%e 10 11 11
%e 11 15 0
%e 12 16 0
%o (C++) See Links section.
%Y See and A109812, A303767 and A370790 for similar sequences.
%Y Cf. A370794 (inverse).
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Mar 02 2024