login
If the ternary expansion of n starts with the digit 1, then replace 2's by 0's and vice versa; if the ternary expansion of n starts with the digit 2, then replace 1's by 0's and vice versa; a(0) = 0.
4

%I #12 Apr 02 2023 10:27:43

%S 0,1,2,5,4,3,7,6,8,17,16,15,14,13,12,11,10,9,22,21,23,19,18,20,25,24,

%T 26,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,

%U 31,30,29,28,27,67,66,68,64,63,65,70,69,71,58,57,59,55,54

%N If the ternary expansion of n starts with the digit 1, then replace 2's by 0's and vice versa; if the ternary expansion of n starts with the digit 2, then replace 1's by 0's and vice versa; a(0) = 0.

%C Leading zeros in ternary expansions are ignored.

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

%H Rémy Sigrist, <a href="/A361945/b361945.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 a(n) = n iff n belongs to A048328.

%F a(n) = A171960(n) when A122586(n) = 1.

%e The first terms, in decimal and in ternary, are:

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

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

%e 0 0 0 0

%e 1 1 1 1

%e 2 2 2 2

%e 3 5 10 12

%e 4 4 11 11

%e 5 3 12 10

%e 6 7 20 21

%e 7 6 21 20

%e 8 8 22 22

%e 9 17 100 122

%e 10 16 101 121

%e 11 15 102 120

%e 12 14 110 112

%e 13 13 111 111

%e 14 12 112 110

%e 15 11 120 102

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

%Y Cf. A048328 (fixed points), A122586, A171960.

%K nonn,base,easy

%O 0,3

%A _Rémy Sigrist_, Mar 31 2023