cp's OEIS Frontend

A343312 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).

%I A343312 #16 Apr 15 2021 15:24:19
%S A343312 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 A343312 22,33,21,35,19,36,23,31,24,29,25,30,26,28,27,41,121,42,119,43,120,44,
%U A343312 115,47,118,45,113,49,114,48,116,46,117,50,103,59,112,51,101
%N A343312 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 A343312 This sequence is a permutation of the nonnegative integers (with inverse A343313):
%C A343312 - we can always extend the sequence with a member of A003462 sufficiently large,
%C A343312 - so the sequence is infinite and unbounded,
%C A343312 - once we have a k-digit number and before introducing a number with more than k digits, we must use A003462(k),
%C A343312 - so we have infinitely many terms of A003462 in this sequence,
%C A343312 - 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 A343312 Apparently:
%C A343312 - the sequence preserves the number of digits in balanced ternary representation (A134021),
%C A343312 - fixed points correspond to 0 and A007051.
%H A343312 Rémy Sigrist, <a href="/A343312/b343312.txt">Table of n, a(n) for n = 0..9842</a>
%H A343312 Rémy Sigrist, <a href="/A343312/a343312.png">Scatterplot of the sequence for n = 0..3^9</a>
%H A343312 Rémy Sigrist, <a href="/A343312/a343312.gp.txt">PARI program for A343312</a>
%H A343312 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A343312 A343229(a(n)) AND A343228(a(n+1)) = A343228(a(n+1)) (where AND denotes the bitwise AND operator).
%e A343312 The first terms, alongside their balanced ternary representation (with "T" instead of digits "-1"), are:
%e A343312   n   a(n)  bter(a(a))
%e A343312   --  ----  ----------
%e A343312    0     0           0
%e A343312    1     1           1
%e A343312    2     2          1T
%e A343312    3     4          11
%e A343312    4     3          10
%e A343312    5     5         1TT
%e A343312    6    13         111
%e A343312    7     6         1T0
%e A343312    8    11         11T
%e A343312    9     7         1T1
%e A343312   10    12         110
%e A343312   11     8         10T
%e A343312   12    10         101
%e A343312   13     9         100
%e A343312   14    14        1TTT
%e A343312   15    40        1111
%e A343312   16    15        1TT0
%e A343312   17    38        111T
%o A343312 (PARI) See Links section.
%Y A343312 Cf. A003462, A007051, A134021, A343228, A343229, A343313 (inverse).
%K A343312 nonn,base,look
%O A343312 0,3
%A A343312 _Rémy Sigrist_, Apr 11 2021