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A285471 A labyrinth-sequence where the entry is the first digit of the sequence and the exit at infinity. (How to move in the labyrinth is explained in the Comments and Example sections).

%I A285471 #15 Apr 24 2017 14:56:59
%S A285471 1,3,0,5,7,9,2,20,13,15,4,18,31,38,33,35,21,8,34,37,23,17,19,6,11,78,
%T A285471 28,50,51,25,61,39,29,81,10,16,53,27,80,14,55,57,22,59,83,30,58,85,65,
%U A285471 12,43,70,40,71,32,52,41,73,45,47,72,42,75,49,24,54,77
%N A285471 A labyrinth-sequence where the entry is the first digit of the sequence and the exit at infinity. (How to move in the labyrinth is explained in the Comments and Example sections).
%C A285471 The aim is to enter the labyrinth on the first digit (here 1) and to visit each digit of the sequence exactly once. To move in the labyrinth is easy: when you land on an odd digit "o", you jump to the right over "o" digits; and when you land on an even digit "e", you jump to the left over "e" digits; as 0 (zero) is an even digit, if you land on a 0 you simply "slide" on the next digit to the left.
%C A285471 Autonomous "loops" inside the labyrinth are not allowed; this loop, for instance, is forbidden: [1,0,3,x,x,x,4].
%C A285471 The sequence is started with a(1) = 1 and always extended with the smallest possible integer not yet in the sequence.
%H A285471 Lars Blomberg, <a href="/A285471/b285471.txt">Table of n, a(n) for n = 1..800</a> (Due to possible future backtracking, the last few terms may not be correct.)
%H A285471 Lars Blomberg, <a href="/A285471/a285471.png">Illustration of 800 terms</a>
%H A285471 Lars Blomberg, <a href="/A285471/a285471_1.png">Illustration of the labyrinth path for 800 terms</a>
%H A285471 Lars Blomberg, <a href="/A285471/a285471_2.png">Illustration of the difference between the labyrinth path and the line y=x for 800 terms</a>
%H A285471 Lars Blomberg, <a href="/A285471/a285471.cs.txt">C# program for computing the terms</a>
%e A285471 The sequence starts with 1,3,0,5,7,9,2,20,13,15,4,18,...
%e A285471 You land on the first "1" and then jump over 1 digit to the right: you land on 0; this 0 forces you to "slide" on the prior digit 3 (as 0 is even); this 3 sends you to the right, jumping over 3 digits: you land on 9; this 9 sends you to the right again, jumping over 9 digits: you land on 8; this 8 sends you to the left (as 8 is even), jumping over 8 digits: you land on the isolated integer 2; this 2 sends you again to the left, jumping over 2 digits: you land on 5; 5 sends you to the right (as 5 is odd), jumping over 5 digits: you land on 1; etc. All digits of the sequence will be visited once in this way.
%K A285471 nonn,base,nice
%O A285471 1,2
%A A285471 _Eric Angelini_ and _Lars Blomberg_, Apr 19 2017
%E A285471 Corrected a(26) and beyond and clarified the Comment by _Lars Blomberg_, Apr 24 2017