Infinite Motel

[Ray Chandler]

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}

Reverse:
{1, 2, 4, 7, 11, 5, 13, 20, 10, 22, 8, 24, 3, 26, 40, 23, 42, 19, 44, 17, 46, \
15, 48, 12, 50, 6, 52, 79, 49, 81, 45, 83, 41, 85, 38, 87, 36, 89, 34, 91, \
32, 93, 30, 95, 28, 97, 25, 99, 18, 101, 14, 103, 155, 100, 157, 96, 159, 92, \
161, 88, 163, 84, 165, 80, 167, 77, 169, 75, 171, 73, 173, 71, 175, 69, 177, \
67, 179, 65, 181, 63, 183, 61, 185, 59, 187, 57, 189, 55, 191, 53, 193, 47, \
195, 39, 197, 35, 199, 31, 201, 27}

Incremental steps:
{1, 1, 2, 3, 4, 6, 8, 7, 10, 12, 14, 16, 21, 23, 14, 17, 19, 23, 25, 27, 29, \
31, 33, 36, 38, 44, 46, 27, 30, 32, 36, 38, 42, 44, 47, 49, 51, 53, 55, 57, \
59, 61, 63, 65, 67, 69, 72, 74, 81, 83, 87, 89, 52, 55, 57, 61, 63, 67, 69, \
73, 75, 79, 81, 85, 87, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, \
112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, \
146, 148, 156, 158, 162, 164, 168, 170, 174}

Cumulative steps:
{1, 2, 4, 7, 11, 17, 25, 32, 42, 54, 68, 84, 105, 128, 142, 159, 178, 201, \
226, 253, 282, 313, 346, 382, 420, 464, 510, 537, 567, 599, 635, 673, 715, \
759, 806, 855, 906, 959, 1014, 1071, 1130, 1191, 1254, 1319, 1386, 1455, \
1527, 1601, 1682, 1765, 1852, 1941, 1993, 2048, 2105, 2166, 2229, 2296, 2365, \
2438, 2513, 2592, 2673, 2758, 2845, 2935, 3027, 3121, 3217, 3315, 3415, 3517, \
3621, 3727, 3835, 3945, 4057, 4171, 4287, 4405, 4525, 4647, 4771, 4897, 5025, \
5155, 5287, 5421, 5557, 5695, 5835, 5981, 6129, 6285, 6443, 6605, 6769, 6937, \
7107, 7281}



-----Original Message-----
From: Jack Brennen [mailto:jb at brennen.net] 
Sent: Wednesday, August 31, 2005 12:22 PM
To: seqfan at ext.jussieu.fr
Subject: Re: Infinite Motel


I tried to look at extending/analyzing the sequence, but I hit a problem right away...  I come up with a slightly
different sequence (which I'm sure diverges greatly as you continue):

You show:
  1,2,13,3,6,26,4,11,408,9,5,24,7,51,22,102,20,49,18,8,205,10,16,...
I show:
  1,2,13,3,6,26,4,11,205,9,5,24,7,51,22,102,20,49,18,8,410,10,16,...
                     ^^^                               ^^^