cp's OEIS Frontend

A379657 The nonadjacent form of a(n) is obtained by inserting a digit 0 before each nonzero digit in the balanced ternary expansion of n.

%I A379657 #10 Dec 30 2024 16:07:38
%S A379657 0,1,3,2,5,11,6,13,7,4,9,19,10,21,43,22,45,23,12,25,51,26,53,27,14,29,
%T A379657 15,8,17,35,18,37,75,38,77,39,20,41,83,42,85,171,86,173,87,44,89,179,
%U A379657 90,181,91,46,93,47,24,49,99,50,101,203,102,205,103,52,105
%N A379657 The nonadjacent form of a(n) is obtained by inserting a digit 0 before each nonzero digit in the balanced ternary expansion of n.
%C A379657 A permutation of the nonnegative integers with inverse A379658.
%H A379657 Rémy Sigrist, <a href="/A379657/b379657.txt">Table of n, a(n) for n = 0..10000</a>
%H A379657 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, pages 61-62.
%H A379657 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary">Balanced ternary</a>
%H A379657 Wikipedia, <a href="https://en.wikipedia.org/wiki/Non-adjacent_form">Non-adjacent form</a>
%H A379657 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A379657 A334913(a(n)) = A065363(n).
%e A379657 The first terms are:  n   a(n)  bter(n)  naf(a(n))
%e A379657   --  ----  -------  ---------
%e A379657    0     0        0          0
%e A379657    1     1        1          1
%e A379657    2     3       1T        10T
%e A379657    3     2       10         10
%e A379657    4     5       11        101
%e A379657    5    11      1TT      10T0T
%e A379657    6     6      1T0       10T0
%e A379657    7    13      1T1      10T01
%e A379657    8     7      10T       100T
%e A379657    9     4      100        100
%e A379657   10     9      101       1001
%e A379657   11    19      11T      1010T
%e A379657   12    10      110       1010
%o A379657 (PARI) a(n) = { my (v = 0, d, b = 1); while (n, d = centerlift(Mod(n, 3)); n = (n-d)/3;
%o A379657  v += d * b; b *= if (d, 4, 2);); v; }
%Y A379657 See A048680 for a similar sequence.
%Y A379657 Cf. A065363, A334913, A379658 (inverse).
%K A379657 nonn,base
%O A379657 0,3
%A A379657 _Rémy Sigrist_, Dec 29 2024