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Lexicographically earliest sequence of distinct integers such that a(0) = 0 and the balanced ternary expansions of two consecutive terms differ by a single digit, as far to the right as possible.
1

%I #19 May 02 2021 04:17:38

%S 0,-1,1,-2,-4,-3,3,2,4,-5,-7,-6,-12,-13,-11,-8,-10,-9,9,8,10,7,5,6,12,

%T 11,13,-14,-16,-15,-21,-22,-20,-17,-19,-18,-36,-37,-35,-38,-40,-39,

%U -33,-34,-32,-23,-25,-24,-30,-31,-29,-26,-28,-27,27,26,28,25,23,24

%N Lexicographically earliest sequence of distinct integers such that a(0) = 0 and the balanced ternary expansions of two consecutive terms differ by a single digit, as far to the right as possible.

%C This sequence has similarities with A003188 and with A341055.

%C A007949 gives the positions of the digit that is altered from one term to the other.

%C To compute a(n):

%C - consider the ternary representation of A128173(n),

%C - replace 1's by -1's and 2's by 1's,

%C - convert back to decimal.

%H Rémy Sigrist, <a href="/A343766/b343766.txt">Table of n, a(n) for n = 0..6560</a>

%H Rémy Sigrist, <a href="/A343766/a343766.png">Scatterplot of the first 3^10 terms</a>

%H Rémy Sigrist, <a href="/A343766/a343766.gp.txt">PARi program for A343766</a>

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

%F a(n) = -A117966(A128173(n)).

%F Sum_{k=0..n-1} sign(a(k)) = -A081134(n).

%F Sum_{k=0..n} a(k) = 0 iff n belongs to A024023.

%e The first terms, alongside their balanced ternary expansion (with T's denoting -1's), are:

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

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

%e 0 0 0

%e 1 -1 T

%e 2 1 1

%e 3 -2 T1

%e 4 -4 TT

%e 5 -3 T0

%e 6 3 10

%e 7 2 1T

%e 8 4 11

%e 9 -5 T11

%e 10 -7 T1T

%e 11 -6 T10

%e 12 -12 TT0

%e 13 -13 TTT

%e 14 -11 TT1

%o (PARI) See Links section.

%Y Cf. A003188, A007949, A024023, A081134, A128173, A341055.

%K sign,base

%O 0,4

%A _Rémy Sigrist_, Apr 28 2021