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A342224 The n-th and a(n)-th points of the curve (A334474, A334475) are symmetrical with respect to the line X=Y.

%I A342224 #14 Mar 07 2021 14:41:49
%S A342224 0,2,1,3,8,9,7,6,4,5,15,11,14,13,12,10,31,32,30,29,33,35,34,28,27,26,
%T A342224 25,24,23,19,18,16,17,20,22,21,63,62,59,58,60,61,42,44,43,47,46,45,57,
%U A342224 55,56,51,54,53,52,49,50,48,39,38,40,41,37,36,121,122,120
%N A342224 The n-th and a(n)-th points of the curve (A334474, A334475) are symmetrical with respect to the line X=Y.
%C A342224 In other words, a(n) is the unique k such that A334474(n) = A334475(k) and A334474(k) = A334475(n).
%C A342224 This sequence is a self-inverse permutation of the nonnegative integers.
%H A342224 Rémy Sigrist, <a href="/A342224/b342224.txt">Table of n, a(n) for n = 0..8255</a>
%H A342224 Rémy Sigrist, <a href="/A342224/a342224.gp.txt">PARI program for A342224</a>
%H A342224 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A342224 a(n) < A007582(k) for any n < A007582(k).
%e A342224 The curve (A334474, A334475) begins as follows on a hexagonal lattice:
%e A342224                  +
%e A342224                 /5\
%e A342224                /   \
%e A342224               +4    +6
%e A342224                \     \
%e A342224                 \     \
%e A342224            +    3+     +7
%e A342224           /1\   /     /
%e A342224          /   \ /     /
%e A342224         +     +     +----+
%e A342224          0     2     8    9
%e A342224 - so a(0) = 0,
%e A342224      a(1) = 2,
%e A342224      a(3) = 3,
%e A342224      a(4) = 8,
%e A342224      a(5) = 9,
%e A342224      a(6) = 7.
%o A342224 (PARI) See Links section.
%Y A342224 See A342217 and A342218 for similar sequences.
%Y A342224 Cf. A007582, A334474, A334475.
%K A342224 nonn
%O A342224 0,2
%A A342224 _Rémy Sigrist_, Mar 06 2021