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If the ternary expansion of n starts with a 1, replace 1's by 2's, 2's by 0's, 0's by 1's, if it starts with a 2, replace 2's by 1's, 1's by 0's, 0's by 2's.
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%I #10 Mar 18 2024 13:23:58

%S 0,2,1,7,8,6,5,3,4,22,23,21,25,26,24,19,20,18,17,15,16,11,9,10,14,12,

%T 13,67,68,66,70,71,69,64,65,63,76,77,75,79,80,78,73,74,72,58,59,57,61,

%U 62,60,55,56,54,53,51,52,47,45,46,50,48,49,35,33,34,29,27

%N If the ternary expansion of n starts with a 1, replace 1's by 2's, 2's by 0's, 0's by 1's, if it starts with a 2, replace 2's by 1's, 1's by 0's, 0's by 2's.

%C This sequence is a self-inverse permutation of the nonnegative integers.

%H Rémy Sigrist, <a href="/A371268/b371268.txt">Table of n, a(n) for n = 0..6560</a>

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

%F A371256(a(n)) = A371256(n).

%e The first terms, in decimal and in base 3, are:

%e n a(n) ter(n) ter(a(n))

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

%e 0 0 0 0

%e 1 2 1 2

%e 2 1 2 1

%e 3 7 10 21

%e 4 8 11 22

%e 5 6 12 20

%e 6 5 20 12

%e 7 3 21 10

%e 8 4 22 11

%e 9 22 100 211

%e 10 23 101 212

%e 11 21 102 210

%e 12 25 110 221

%e 13 26 111 222

%e 14 24 112 220

%e 15 19 120 201

%o (PARI) a(n) = { my (d = digits(n, 3)); if (#d, d = if (d[1]==1, apply(v -> [1, 2, 0][1+v], d), apply(v -> [2, 0, 1][1+v], d));); fromdigits(d, 3); }

%Y See A004488 and A361945 for similar sequences.

%Y Cf. A338246, A371256.

%K nonn,base,easy

%O 0,2

%A _Rémy Sigrist_, Mar 16 2024