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A307404 Base-5 based twisted permutation of the nonnegative integers - variant "Ln". 3
0, 1, 2, 3, 4, 9, 8, 7, 6, 5, 10, 15, 20, 21, 16, 11, 12, 13, 14, 19, 18, 17, 22, 23, 24, 49, 48, 47, 42, 43, 44, 39, 38, 37, 36, 41, 46, 45, 40, 35, 30, 31, 32, 33, 34, 29, 28, 27, 26, 25, 50, 75, 100, 101, 76, 51, 52, 53, 54, 79, 78, 77, 102 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Base-5 variant of Knuth's A220952. The definition of the sequence by an adjacency diagram is the same as in A220952, except that the diagram for the sequence here is:

  .

  (0,4)--(1,4)  (2,4)--(3,4)  (4,4)

    |      |      |      |      |

    |      |      |      |      |

  (0,3)  (1,3)  (2,3)  (3,3)  (4,3)

    |      |      |      |      |

    |      |      |      |      |

  (0,2)  (1,2)  (2,2)  (3,2)--(4,2)

    |      |      |

    |      |      |

  (0,1)  (1,1)  (2,1)--(3,1)--(4,1)

    |      |                    |

    |      |                    |

  (0,0)  (1,0)--(2,0)--(3,0)--(4,0)

  .

Conjecture: As in A220952, it can be proved (a) that every positive integer is adjacent to exactly two nonnegative integers, and (b) that with this definition of adjacency, the nonnegative integers form a path starting with 0.

The adjacency definition implies that the terms, when written with 3 base-5 digits, define the coordinates of a self-avoiding, space-filling path in a 5 X 5 X 5 cube. All 3 orthogonal projections to the plane are congruent to the diagram above. This property is maintained in the 4th, 5th ... dimension.

The variants of such adjacency diagrams may be distinguished by letter codes, in this case "Ln" with "L" for the path (0,0)...(2,1), and "n" for the path in the upper right corner which has the same shape as the inner structure (1,1)...(3,3) of Knuths's A220952.

LINKS

Table of n, a(n) for n=0..62.

Georg Fischer, Repository of programs for related sequences, (gen_paths.pl)

EXAMPLE

In base-5, the terms for the path in two dimensions are 0, 1, 2, 3, 4, 14, 13, 12, 11, 10, 20, 30, 40, 41, 31, 21, 22, 23, 24, 34, 33, 32, 42, 43, 44.

CROSSREFS

Cf. A220952 (main entry, "Hn"), A307403 ("Hs"), A307405 ("Ls"), A307406 (number of variants per odd base).

Sequence in context: A064478 A111798 A249543 * A307405 A115305 A210747

Adjacent sequences:  A307401 A307402 A307403 * A307405 A307406 A307407

KEYWORD

nonn,base,easy

AUTHOR

Georg Fischer, Apr 07 2019

STATUS

approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)