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A342218 The n-th and a(n)-th points of the Peano curve (A163528, A163529) are symmetrical with respect to the line X=Y.

%I A342218 #19 Mar 07 2021 17:11:03
%S A342218 0,5,6,7,4,1,2,3,8,45,50,51,52,49,46,47,48,53,54,59,60,61,58,55,56,57,
%T A342218 62,63,68,69,70,67,64,65,66,71,36,41,42,43,40,37,38,39,44,9,14,15,16,
%U A342218 13,10,11,12,17,18,23,24,25,22,19,20,21,26,27,32,33,34,31
%N A342218 The n-th and a(n)-th points of the Peano curve (A163528, A163529) are symmetrical with respect to the line X=Y.
%C A342218 In other words, a(n) is the unique k such that A163528(n) = A163529(k) and A163528(k) = A163529(n).
%C A342218 This sequence is a self-inverse permutation of the nonnegative integers.
%H A342218 Rémy Sigrist, <a href="/A342218/b342218.txt">Table of n, a(n) for n = 0..6560</a>
%H A342218 Rémy Sigrist, <a href="/A342218/a342218.gp.txt">PARI program for A342218</a>
%H A342218 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%F A342218 a(n) = n iff n belongs to A338086.
%F A342218 a(n) < 9^k for any n < 9^k.
%e A342218 The Peano curve (A163528, A163529) begins as follows:
%e A342218        +-----+-----+
%e A342218        |6     7     8
%e A342218        |
%e A342218        +-----+-----+
%e A342218         5     4    |3
%e A342218                    |
%e A342218        +-----+-----+
%e A342218         0     1     2
%e A342218 - so a(0) = 0,
%e A342218      a(1) = 5,
%e A342218      a(2) = 6,
%e A342218      a(3) = 7,
%e A342218      a(4) = 4,
%e A342218      a(8) = 8.
%o A342218 (PARI) See Links section.
%o A342218 (PARI) my(table=[0,5,6,7,4,1,2,3,8]); a(n) = fromdigits(apply(d->table[d+1], digits(n,9)), 9); \\ _Kevin Ryde_, Mar 07 2021
%Y A342218 See A342217 and A342224 for similar sequences.
%Y A342218 Cf. A163528, A163529, A338086.
%K A342218 nonn,look
%O A342218 0,2
%A A342218 _Rémy Sigrist_, Mar 05 2021