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 A334577 a(n) is the Y-coordinate of the n-th point of the space filling curve P defined in Comments section; sequence A334576 gives X-coordinates. 2
 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 1, 1, 2, 3, 4, 4, 4, 5, 6, 6, 5, 4, 3, 3, 3, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 2, 3, 4, 4, 4, 5, 5, 5, 6, 7, 8, 8, 8, 9, 10, 10, 9, 8, 8, 8, 8, 9, 9, 9, 10, 11, 12, 12, 12, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The space filling curve P corresponds to the midpoint curve of the alternate paperfolding curve and can be built as follows: - we define the family {P_k, k > 0}:     - P_1 corresponds to the points (0, 0), (1, 0), (2, 0) and (2, 1), in that order:                     +                     |                     |           +----+----+          O     - for any k > 0, P_{n+1} is built from four copies of P_n as follows:                                             +                                             |A                 +                           |                C|                   +----+  |          A     B|    --->           |C  B|  |B  C         +-------+                   +    |  +----+-+        O                           C|    |        C|                              A     B|   A|  A     B|                             +-------+    +-+-------+                            O - the space filling curve P is the limit of P_k as k tends to infinity. We can also describe the space filling curve P by mean of an L-system (see Links section). LINKS Rémy Sigrist, Table of n, a(n) for n = 0..4095 Joerg Arndt, L-system corresponding to P Kevin Ryde, Iterations of the Alternate Paperfolding Curve Rémy Sigrist, PARI program for A334577 FORMULA a(n+1) = (A020990(n) + A020990(n+1) - 1)/2 for any n >= 0. EXAMPLE The first points of the space filling curve P are as follows:       6|                                  20...21        |                                  |    |       5|                                  19   22        |                                  |    |       4|                        16...17...18   23        |                        |              |       3|                        15   26...25...24        |                        |    |       2|              4....5    14   27...28...29        |              |    |    |              |       1|              3    6    13...12...11   30        |              |    |              |    |       0|    0....1....2    7....8....9....10   31..        |     ---+----------------------------------------     y/x|    0    1    2    3    4    5    6    7 - hence a(15) = a(24) = a(25) = a(26) = 3. PROG (PARI) See Links section. CROSSREFS Cf. A020990, A334576. Sequence in context: A255124 A030619 A016370 * A219494 A334221 A089069 Adjacent sequences:  A334574 A334575 A334576 * A334578 A334579 A334580 KEYWORD nonn AUTHOR Rémy Sigrist, May 06 2020 STATUS approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)