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A379658 The balanced ternary expansion of a(n) is obtained by removing a digit 0 before each nonzero digit in the nonadjacent form of n.

%I A379658 #9 Dec 30 2024 16:07:33
%S A379658 0,1,3,2,9,4,6,8,27,10,12,5,18,7,24,26,81,28,30,11,36,13,15,17,54,19,
%T A379658 21,23,72,25,78,80,243,82,84,29,90,31,33,35,108,37,39,14,45,16,51,53,
%U A379658 162,55,57,20,63,22,69,71,216,73,75,77,234,79,240,242,729
%N A379658 The balanced ternary expansion of a(n) is obtained by removing a digit 0 before each nonzero digit in the nonadjacent form of n.
%C A379658 A permutation of the nonnegative integers with inverse A379657.
%H A379658 Rémy Sigrist, <a href="/A379658/b379658.txt">Table of n, a(n) for n = 0..10000</a>
%H A379658 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, pages 61-62.
%H A379658 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%H A379658 Wikipedia, <a href="https://en.wikipedia.org/wiki/Non-adjacent_form">Non-adjacent form</a>
%H A379658 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A379658 A065363(a(n)) = A334913(n).
%e A379658 The first terms are:
%e A379658   n   a(n)  naf(n)  bter(a(n))
%e A379658   --  ----  ------  ----------
%e A379658    0     0       0           0
%e A379658    1     1       1           1
%e A379658    2     3      10          10
%e A379658    3     2     10T          1T
%e A379658    4     9     100         100
%e A379658    5     4     101          11
%e A379658    6     6    10T0         1T0
%e A379658    7     8    100T         10T
%e A379658    8    27    1000        1000
%e A379658    9    10    1001         101
%e A379658   10    12    1010         110
%e A379658   11     5   10T0T         1TT
%e A379658   12    18   10T00        1T00
%o A379658 (PARI) a(n) = { my (v = 0, t = 1, d); while (n, if (n%2, n -= d = 2 - (n%4); v += d*t; t /= 3;); n \= 2; t *= 3;); return (v); }
%Y A379658 See A048679 for a similar sequence.
%Y A379658 Cf. A065363, A334913, A379657 (inverse).
%K A379658 nonn,base
%O A379658 0,3
%A A379658 _Rémy Sigrist_, Dec 29 2024