cp's OEIS Frontend

A341121 a(n) is the Y-coordinate of the n-th point of the space filling curve C defined in Comments section; A341120 gives X-coordinates.

%I A341121 #10 Feb 09 2021 11:01:06
%S A341121 0,1,1,1,0,0,1,2,2,2,3,4,4,3,3,3,4,4,5,6,6,7,7,7,6,7,7,7,6,6,5,4,4,4,
%T A341121 5,6,6,7,7,7,6,7,7,7,6,6,5,4,4,3,3,3,4,4,3,2,2,2,1,0,0,1,1,1,0,0,1,2,
%U A341121 2,3,3,3,2,3,3,3,2,2,1,0,0,1,1,1,0,0,1
%N A341121 a(n) is the Y-coordinate of the n-th point of the space filling curve C defined in Comments section; A341120 gives X-coordinates.
%C A341121 We define the family {C_n, n >= 0}, as follows:
%C A341121 - C_0 corresponds to the points (0, 0), (0, 1), (1, 1), (2, 1) and (2, 0), in that order:
%C A341121        +---+---+
%C A341121        |       |
%C A341121        +       +
%C A341121       O
%C A341121 - for any n >= 0, C_{n+1} is obtained by arranging 4 copies of C_n as follows:
%C A341121                            + . . . + . . . +
%C A341121                            .   B   .   B   .
%C A341121        + . . . +           .       .       .
%C A341121        .   B   .           .A     C.A     C.
%C A341121        .       .    -->    + . . . + . . . +
%C A341121        .A     C.           .C      .      A.
%C A341121        + . . . +           .      B.B      .
%C A341121       O                    .A      .      C.
%C A341121                            + . . . + . . . +
%C A341121                           O
%C A341121 - the space filling curve C is the limit of C_{2*n} as n tends to infinity.
%H A341121 Rémy Sigrist, <a href="/A341121/b341121.txt">Table of n, a(n) for n = 0..16384</a>
%H A341121 F. M. Dekking, <a href="http://dx.doi.org/10.1016/0001-8708(82)90066-4">Recurrent Sets</a>, Advances in Mathematics, vol. 44, no. 1, 1982.
%H A341121 Rémy Sigrist, <a href="/A341121/a341121.gp.txt">PARI program for A341121</a>
%H A341121 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%F A341121 a(2*n) = A341019(n).
%F A341121 a(4*n) = 2*A341120(n).
%F A341121 a(16*n) = 4*a(n).
%F A341121 a(n) = A059253(n) + A283316(n+1).
%F A341121 A059252(n) = (a(4*n+2)-1)/2.
%e A341121 Points n and their locations X=A341120(n), Y=a(n) begin as follows.  n=7 and n=9 are both at X=3,Y=2, and n=11,n=31 both at X=3,Y=4.
%e A341121       |       |
%e A341121     4 | 16---17   12--11,31
%e A341121       |  |         |    |
%e A341121     3 | 15---14---13   10
%e A341121       |                 |
%e A341121     2 |            8---7,9
%e A341121       |                 |
%e A341121     1 |  1----2----3    6
%e A341121       |  |         |    |
%e A341121   Y=0 |  0         4----5
%e A341121       +--------------------
%e A341121        X=0    1    2    3
%o A341121 (PARI) See Links section.
%Y A341121 Cf. A059252, A341019, A341120.
%K A341121 nonn
%O A341121 0,8
%A A341121 _Kevin Ryde_ and _Rémy Sigrist_, Feb 05 2021