[seqfan] A 10-digits-by-row array
Éric Angelini
bk263401 at skynet.be
Fri Mar 27 17:25:22 CET 2020
Hello SeqFans,
Here is an array I like – it could be easily turned into a sequence for the OEIS (hope it will). This array raises a few questions:
0,1,2,3,4,5,6,7,8,9,
10,23,45,67,89,
12,30,46,57,98,
13,20,47,58,69,
14,25,36,78,90,
15,24,37,80,96,
16,27,38,40,59,
17,26,39,48,50,
18,29,34,56,70,
19,28,35,60,74,
21,43,65,7089,
31,42,68,5079,
32,41,75,6089,
49,51,62,3078,
52,61,73,4089,
53,64,71,2089,
54,63,72,1089,
76,81,92,3045,
79,82,103,456,
83,91,204,567,
84,93,102,576,
85,94,106,237,
86,95,104,273,
87,105,23469,
97,108,23456,
107,234,5689,
109,235,4678,
etc.
The three constraints:
1) Every row is made of exactly 10 distinct digits.
2) Every term in the array is unique.
3) When the array will be completed (the number of terms is limited), we will concatenate its rows (in their order of appearance) and build a sequence: this sequence must be the lexicographically earliest of its kind.
Example:
The first row is obvious: < 0,1,2,3,4,5,6,7,8,9 >
The second row is < 10, 23, 45, 67, 89 > and NOT < 10, 32, 54, 876, 9 > because:
23 lexico-beats 32,
45 lexico-beats 54
67 lexico-beats 876 and
9 was used before.
Now the questions:
How many rows will have the completed array?
How many terms will there be in the sequence (between 0, the first one, and 9876543210, the last one)?
What would be an array like this one, but with prime terms only? Even terms only? Odd terms only?
[Beware, the above array was made by hand and is almost guaranteed to be wrong – but you get the idea].
And if this is old hat, pardon me (the only seq I could Xref is A120125).
P.-S.
This message is also visible here, on my personal weblog:
https://bit.ly/3bwVuSU.
Best,
É.
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