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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. 3

%I #19 Mar 07 2021 17:11:03

%S 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 62,63,68,69,70,67,64,65,66,71,36,41,42,43,40,37,38,39,44,9,14,15,16,

%U 13,10,11,12,17,18,23,24,25,22,19,20,21,26,27,32,33,34,31

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

%C In other words, a(n) is the unique k such that A163528(n) = A163529(k) and A163528(k) = A163529(n).

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

%H Rémy Sigrist, <a href="/A342218/b342218.txt">Table of n, a(n) for n = 0..6560</a>

%H Rémy Sigrist, <a href="/A342218/a342218.gp.txt">PARI program for A342218</a>

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

%F a(n) = n iff n belongs to A338086.

%F a(n) < 9^k for any n < 9^k.

%e The Peano curve (A163528, A163529) begins as follows:

%e +-----+-----+

%e |6 7 8

%e |

%e +-----+-----+

%e 5 4 |3

%e |

%e +-----+-----+

%e 0 1 2

%e - so a(0) = 0,

%e a(1) = 5,

%e a(2) = 6,

%e a(3) = 7,

%e a(4) = 4,

%e a(8) = 8.

%o (PARI) See Links section.

%o (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 See A342217 and A342224 for similar sequences.

%Y Cf. A163528, A163529, A338086.

%K nonn,look

%O 0,2

%A _Rémy Sigrist_, Mar 05 2021

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)