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A285471
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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).
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5
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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, 28, 50, 51, 25, 61, 39, 29, 81, 10, 16, 53, 27, 80, 14, 55, 57, 22, 59, 83, 30, 58, 85, 65, 12, 43, 70, 40, 71, 32, 52, 41, 73, 45, 47, 72, 42, 75, 49, 24, 54, 77
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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.
Autonomous "loops" inside the labyrinth are not allowed; this loop, for instance, is forbidden: [1,0,3,x,x,x,4].
The sequence is started with a(1) = 1 and always extended with the smallest possible integer not yet in the sequence.
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LINKS
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EXAMPLE
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The sequence starts with 1,3,0,5,7,9,2,20,13,15,4,18,...
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.
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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EXTENSIONS
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Corrected a(26) and beyond and clarified the Comment by Lars Blomberg, Apr 24 2017
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STATUS
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approved
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