`Hello SeqFan
and Math-Fun,`

`(dont
know if this is of interest)`

`1, 2, 1, 3, 2, 4, 5, 3, 6, 7,
4, 8, 5, 9, 10, 6, 11, 7, 12, 13, 8, 14, 15, 9, 16, 10, 17, 18, 11, 19, 20, 12,
21, 13, ...`

`This sequence displays every positive integer exactly twice,
and the gap between the two occurrences of n contains exactly n other values.
The first occurrence of n precedes the first occurrence of n+1. (cont.) [This is OEIS
`A026272

`What about a similar sequence displaying every
positive integer exactly three times?
We must drop the constraint The first occurrence of n precedes the first
occurrence of n+1 and replace it by Always fill the first hole with the smallest available integer
not used so far.`

`Lets start with the three 1s (a dot represents a
hole which will be filled in the future):`

**1**` .`` 1 . 1 . . . . . . . . . `

`Can we fill the first hole with a 2? No -- we would
bump immediately into a 1:`

`1 2
1 . 1
. . . . . . . . .`

`Can we fill the first hole with a 3 instead? Yes,
there is room for the three 3s:`

`1 3 1 . 1 3 . . . 3 . . . .`

`Can we fill the first hole with a 2? (smallest available integer not used so far)? No -- we would
bump into a 3 at
the end:`

`1 3 1 2 1 3 2 . . 3 . . . .`

`Can we fill the first hole with a 4 instead? Yes,
there is room for the three 4s:`

`1 3 1 4 1 3 . . 4 3 . . . 4`

`Can we fill the first hole with a 2? (smallest available integer not used so far)? No -- we would
bump immediately into a 3:`

`1 3 1 4 1 3 2 . 4 3 . . . 4`

`Can we fill the first hole with a 5 instead? Yes,
there is room for the three 5s:`

`1 3 1 4 1 3 5 . 4 3 . . 5 4 . . . . 5`

`Can we fill the first hole with a 2? (smallest available integer not used so far)? No -- we would
bump into a 4 at
the end:`

`1 3 1 4 1 3 5 2 4 3 2 . 5 4 . . . . 5`

`Can we fill the first hole with a 6 instead? Yes,
there is room for the three 6s:`

`1 3 1 4 1 3 5 6
4 3 . . 5 4 6
. . . 5 . . 6`

`Can we fill the first hole with a 2? (smallest available integer not used so far)? No -- we would
bump immediately into a 4:`

`1 3 1 4 1 3 5 6 4 3 2 . 5 4 6 . . . 5 . . 6`

`Can we fill the first hole with a 7 instead? No, we
would bump immediately into a 5:`

`1 3 1 4 1 3 5 6 4 3 7 . 5 4 6 . . . 5 .
. 6`

`Can we fill the first hole with a
8 instead? Yes, there is room for the three 8s:`

`1 3 1 4 1 3 5 6 4 3 8 . 5 4 6 . . . 5 8 . 6 . . . . . .
8`

`Can we fill the first hole with a 2 or a 7 or a
9? No, but with a 10 instead, yes. Etc.`

`After a few more steps the
sequence will look like this, if I didnt mistake (on the waiting shelf is
15 -- note that 2 and 7 have found their places):`

`1 3 1 4 1 3 5 6 4 3 8 10 5 4 6 7 9 11 5 8 13 6 10 7 2
12 9 2 8 11 2 7 14 10 13 16 9 . 12 .
. 11 . . . . . 14 13 . . 12 16 . . .`

`Questions:`

`- Will all triplets of integers appear sooner or later
in the sequence?`

`- If we define k
as the number of occurrences of an integer, the above sequence could be called
the 3-Kimberlike sequence (it deals
with triplets), and `A026272

`Best,`

`Ι. `