A361747 - OEIS

%I #8 Mar 24 2023 18:00:50

%S 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 27,28,29,30,31,32,33,34,35,36,37,38,39,40,43,41,42,44,45,46,47,48,49,

%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67

%N 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 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 Table of initial terms (T is a digit of the value -1):

%e   n | a(n) |  BAL

%e  ---+------+-------

%e   1 |    1 |    1

%e   2 |    4 |   11

%e   3 |    2 |   1T

%e   4 |    3 |   10

%e   5 |    6 |  1T0

%e   6 |    5 |  1TT

%e   7 |    7 |  1T1

%e   8 |    8 |  10T

%e   9 |    9 |  100

%e  10 |   10 |  101

%e  11 |   11 |  11T

%e  12 |   12 |  110

%e  13 |   13 |  111

%e  14 |   16 | 1TT1

%e  15 |   14 | 1TTT

%e  16 |   15 | 1TT0

%e  17 |   17 | 1T0T

%e  18 |   18 | 1T00

%e  19 |   19 | 1T01

%e  20 |   20 | 1T1T

%K base,nonn

%O 1,2

%A _Jodi Spitz_, Mar 22 2023