%I #15 Apr 24 2017 14:56:59
%S 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 28,50,51,25,61,39,29,81,10,16,53,27,80,14,55,57,22,59,83,30,58,85,65,
%U 12,43,70,40,71,32,52,41,73,45,47,72,42,75,49,24,54,77
%N 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 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 Autonomous "loops" inside the labyrinth are not allowed; this loop, for instance, is forbidden: [1,0,3,x,x,x,4].
%C The sequence is started with a(1) = 1 and always extended with the smallest possible integer not yet in the sequence.
%H 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 Lars Blomberg, <a href="/A285471/a285471.png">Illustration of 800 terms</a>
%H Lars Blomberg, <a href="/A285471/a285471_1.png">Illustration of the labyrinth path for 800 terms</a>
%H 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 Lars Blomberg, <a href="/A285471/a285471.cs.txt">C# program for computing the terms</a>
%e The sequence starts with 1,3,0,5,7,9,2,20,13,15,4,18,...
%e 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 nonn,base,nice
%O 1,2
%A _Eric Angelini_ and _Lars Blomberg_, Apr 19 2017
%E Corrected a(26) and beyond and clarified the Comment by _Lars Blomberg_, Apr 24 2017