This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307403 #11 Apr 28 2019 12:16:43
%S A307403 0,1,2,3,4,9,14,19,18,13,8,7,12,17,16,11,6,5,10,15,20,21,22,23,24,49,
%T A307403 74,99,98,73,48,47,72,97,96,71,46,45,70,95,90,65,40,35,60,85,80,55,30,
%U A307403 31,56,81,86,61,36,41,66,91,92,67,42,37,62
%N A307403 Base-5 based twisted permutation of the nonnegative integers - variant "Hs".
%C A307403 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:
%C A307403 .
%C A307403 (0,4)--(1,4)--(2,4)--(3,4) (4,4)
%C A307403 | | |
%C A307403 | | |
%C A307403 (0,3) (1,3)--(2,3)--(3,3) (4,3)
%C A307403 | | |
%C A307403 | | |
%C A307403 (0,2) (1,2)--(2,2)--(3,2) (4,2)
%C A307403 | | |
%C A307403 | | |
%C A307403 (0,1) (1,1)--(2,1)--(3,1) (4,1)
%C A307403 | | |
%C A307403 | | |
%C A307403 (0,0) (1,0)--(2,0)--(3,0)--(4,0)
%C A307403 .
%C A307403 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.
%C A307403 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.
%C A307403 The variants of such adjacency diagrams may be distinguished by letter codes, in this case "Hs" with "H" for the vertical bars (0,0..4), (4,0..4), and "s" for the inner structure (1..3,1..3). Knuth's A220952 would then be denoted by "Hn".
%H A307403 Georg Fischer, <a href="https://github.com/gfis/fasces">Repository of programs for related sequences</a>, (<a href="https://github.com/gfis/fasces/blob/master/data/gen_paths.pl">gen_paths.pl</a>)
%e A307403 In base-5, the terms for the path in two dimensions are 0, 1, 2, 3, 4, 14, 24, 34, 33, 23, 13, 12, 22, 32, 31, 21, 11, 10, 20, 30, 40, 41, 42, 43, 44.
%o A307403 (Perl) cf. link.
%Y A307403 Cf. A220952, (main entry, "Hn"), A307404 ("Ln"), A307405 ("Ls"), A307406 (number of variants per odd base).
%K A307403 nonn,base,easy
%O A307403 0,3
%A A307403 _Georg Fischer_, Apr 07 2019