# [seqfan] Re: seqs whose |differences| are 1,2,3,4,...

Ron Hardin rhhardin at att.net
Fri Mar 12 02:43:32 CET 2010

```The shortest (not necessarily lexicographically smallest) such sequence containing all values 1..top for increasing values of top (and no values repeated) are

values 1..1 length=1 :  1
values 1..2 length=2 :  1 2
values 1..3 length=5 :  1 2 4 7 3
values 1..4 length=5 :  1 2 4 7 3
values 1..5 length=13 :  1 2 4 7 3 8 14 21 29 38 28 17 5
values 1..6 length=17 : 1 2 4 7 11 6 12 5 13 22 32 21 33 20 34 19 3
values 1..7 length=17 : 1 2 4 7 11 6 12 5 13 22 32 21 33 20 34 19 3
values 1..8 length=20 : 1 2 4 7 3 8 14 21 29 20 30 41 53 40 54 39 23 6 24 5
values 1..9 length=29 : 1 2 4 7 3 8 14 21 29 20 30 41 53 40 54 39 23 6 24 5 25 46 68 91 115 90 64 37 9
values 1..10 length=36 : 1 2 4 7 3 8 14 21 29 20 30 41 53 40 54 39 23 6 24 5 25 46 68 91 115 140 166 193 165 136 106 75 43 10 44 9
values 1..11 length=37 : 1 2 4 7 3 8 14 21 13 22 12 23 11 24 10 25 9 26 44 63 43 64 42 65 89 114 140 167 195 166 136 105 73 40 6 41 5
values 1..12 length=37 : 1 2 4 7 3 8 14 21 13 22 12 23 11 24 10 25 9 26 44 63 43 64 42 65 89 114 140 167 195 166 136 105 73 40 6 41 5
values 1..13 length=37 : 1 2 4 7 3 8 14 21 13 22 12 23 11 24 10 25 9 26 44 63 43 64 42 65 89 114 140 167 195 166 136 105 73 40 6 41 5
values 1..14 length=37 : 1 2 4 7 3 8 14 21 13 22 12 23 11 24 10 25 9 26 44 63 43 64 42 65 89 114 140 167 195 166 136 105 73 40 6 41 5
values 1..15 length=41 : 1 2 4 7 3 8 14 21 13 22 12 23 11 24 38 53 69 52 34 15 35 56 78 55 31 6 32 5 33 62 92 123 155 122 156 121 85 48 10 49 9

modulo program bugs.  Maybe have more later.

rhhardin at mindspring.com
rhhardin at att.net (either)

```