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Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the digits "-1" in the balanced ternary representation of a(n) correspond to digits "+1" in that of a(n+1).
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%I #16 Apr 15 2021 15:24:19

%S 0,1,2,4,3,5,13,6,11,7,12,8,10,9,14,40,15,38,16,39,17,34,20,37,18,32,

%T 22,33,21,35,19,36,23,31,24,29,25,30,26,28,27,41,121,42,119,43,120,44,

%U 115,47,118,45,113,49,114,48,116,46,117,50,103,59,112,51,101

%N Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the digits "-1" in the balanced ternary representation of a(n) correspond to digits "+1" in that of a(n+1).

%C This sequence is a permutation of the nonnegative integers (with inverse A343313):

%C - we can always extend the sequence with a member of A003462 sufficiently large,

%C - so the sequence is infinite and unbounded,

%C - once we have a k-digit number and before introducing a number with more than k digits, we must use A003462(k),

%C - so we have infinitely many terms of A003462 in this sequence,

%C - for any m with k digits, we have infinitely many terms of A003462 > m in the sequence, each of these terms can be followed by m, so m must eventually appear.

%C Apparently:

%C - the sequence preserves the number of digits in balanced ternary representation (A134021),

%C - fixed points correspond to 0 and A007051.

%H Rémy Sigrist, <a href="/A343312/b343312.txt">Table of n, a(n) for n = 0..9842</a>

%H Rémy Sigrist, <a href="/A343312/a343312.png">Scatterplot of the sequence for n = 0..3^9</a>

%H Rémy Sigrist, <a href="/A343312/a343312.gp.txt">PARI program for A343312</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F A343229(a(n)) AND A343228(a(n+1)) = A343228(a(n+1)) (where AND denotes the bitwise AND operator).

%e The first terms, alongside their balanced ternary representation (with "T" instead of digits "-1"), are:

%e n a(n) bter(a(a))

%e -- ---- ----------

%e 0 0 0

%e 1 1 1

%e 2 2 1T

%e 3 4 11

%e 4 3 10

%e 5 5 1TT

%e 6 13 111

%e 7 6 1T0

%e 8 11 11T

%e 9 7 1T1

%e 10 12 110

%e 11 8 10T

%e 12 10 101

%e 13 9 100

%e 14 14 1TTT

%e 15 40 1111

%e 16 15 1TT0

%e 17 38 111T

%o (PARI) See Links section.

%Y Cf. A003462, A007051, A134021, A343228, A343229, A343313 (inverse).

%K nonn,base,look

%O 0,3

%A _Rémy Sigrist_, Apr 11 2021