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A361747 Lexicographically earliest sequence of distinct positive integers such that a(n) and a(n-1) share at least one identical trit at the same position in their balanced ternary representations.

%I A361747 #8 Mar 24 2023 18:00:50
%S A361747 1,4,2,3,6,5,7,8,9,10,11,12,13,16,14,15,17,18,19,20,21,22,23,24,25,26,
%T A361747 27,28,29,30,31,32,33,34,35,36,37,38,39,40,43,41,42,44,45,46,47,48,49,
%U A361747 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67
%N A361747 Lexicographically earliest sequence of distinct positive integers such that a(n) and a(n-1) share at least one identical trit at the same position in their balanced ternary representations.
%C A361747 Conjecture: Suppose n is the x-th fixed point such that n-1 is not a fixed point. Then for all k such that n < k < (3^(x + 2) + 1)/2, k is also a fixed point.
%e A361747 Table of initial terms (T is a digit of the value -1):
%e A361747   n | a(n) |  BAL
%e A361747  ---+------+-------
%e A361747   1 |    1 |    1
%e A361747   2 |    4 |   11
%e A361747   3 |    2 |   1T
%e A361747   4 |    3 |   10
%e A361747   5 |    6 |  1T0
%e A361747   6 |    5 |  1TT
%e A361747   7 |    7 |  1T1
%e A361747   8 |    8 |  10T
%e A361747   9 |    9 |  100
%e A361747  10 |   10 |  101
%e A361747  11 |   11 |  11T
%e A361747  12 |   12 |  110
%e A361747  13 |   13 |  111
%e A361747  14 |   16 | 1TT1
%e A361747  15 |   14 | 1TTT
%e A361747  16 |   15 | 1TT0
%e A361747  17 |   17 | 1T0T
%e A361747  18 |   18 | 1T00
%e A361747  19 |   19 | 1T01
%e A361747  20 |   20 | 1T1T
%K A361747 base,nonn
%O A361747 1,2
%A A361747 _Jodi Spitz_, Mar 22 2023