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 A307405 #11 Apr 29 2019 21:07:25
%S A307405 0,1,2,3,4,9,8,7,6,5,10,15,20,21,16,11,12,17,22,23,18,13,14,19,24,49,
%T A307405 44,39,38,43,48,47,42,37,36,41,46,45,40,35,30,31,32,33,34,29,28,27,26,
%U A307405 25,50,75,100,101,76,51,52,77,102,103,78,53
%N A307405 Base-5 based twisted permutation of the nonnegative integers - variant "Ls".
%C A307405 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 A307405 .
%C A307405 (0,4)--(1,4) (2,4)--(3,4)--(4,4)
%C A307405 | | |
%C A307405 | | |
%C A307405 (0,3) (1,3) (2,3)--(3,3)--(4,3)
%C A307405 | | |
%C A307405 | | |
%C A307405 (0,2) (1,2) (2,2)--(3,2)--(4,2)
%C A307405 | | |
%C A307405 | | |
%C A307405 (0,1) (1,1) (2,1)--(3,1)--(4,1)
%C A307405 | | |
%C A307405 | | |
%C A307405 (0,0) (1,0)--(2,0)--(3,0)--(4,0)
%C A307405 .
%C A307405 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 A307405 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 A307405 The variants of such adjacency diagrams may be distinguished by letter codes, in this case "Ls" with "L" for the path (0,0)...(2,1), and "s" for the path in the upper right corner which has the same shape as the inner structure (1,1)...(3,3) of A307403 ("Hs").
%H A307405 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 A307405 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, 32, 42, 43, 33, 23, 24, 34, 44.
%o A307405 (Perl) cf. link.
%Y A307405 Cf. A220952 (main entry, "Hn"), A307403 ("Hs"), A307404 ("Ln"), A307406 (number of variants per odd base).
%K A307405 nonn,base,easy
%O A307405 0,3
%A A307405 _Georg Fischer_, Apr 14 2019