Infinite Motel

[Hugo Pfoertner]

Ray Chandler wrote:
> 
> My results agree with Jack's:
> 
> {1, 2, 13, 3, 6, 26, 4, 11, 205, 9, 5, 24, 7, 51, 22, 102, 20, 49, 18, 8, \
> 410, 10, 16, 12, 47, 14, 100, 45, 203, 43, 98, 41, 3277, 39, 96, 37, 201, 35, \
> 94, 15, 33, 17, 408, 19, 31, 21, 92, 23, 29, 25, 199, 27, 90, 819, 88, 197, \
> 86, 406, 84, 195, 82, 1638, 80, 193, 78, 404, 76, 191, 74, 817, 72, 189, 70, \
> 402, 68, 187, 66, 6554, 28, 64, 30, 185, 32, 62, 34, 400, 36, 60, 38, 183, \
> 40, 58, 42, 815, 44, 56, 46, 181, 48, 54}
> 

A related sequence:

Most distant door visited before the door at position n could be
labelled:

      0      2     24      4     11     50      7     22    408     20
     11     48     13    101     46    203     44     99     42     20
    818     22     40     24     97     26    201     95    406     93
    199     91   6552     89    197     87    404     85    195     40
     83     42    816     44     81     46    193     48     79     50
    402     52    191   1637    189    400    187    814    185    398
    183   3275    181    396    179    812    177    394    175   1635
    173    392    171    810    169    390    167  13106     79    165
     81    388     83    163     85    808     87    161     89    386
     91    159     93   1633     95    157     97    384     99    155

Hugo Pfoertner