[seqfan] |a-b| divides concatenation [ab]
Eric Angelini
Eric.Angelini at kntv.be
Mon Sep 20 18:15:15 CEST 2010
Hello SeqFans,
S = 1,144,146,153,156,160,165,176,184,197,274,288,294,315,324,336,352,374, ...
We want:
1) S to be strictly increasing
2) all first diff to be different one from another and not yet present in S
3) a(n+1) to be the smallest integer such that |a(n)-a(n+1)| divides the
concatenation [a(n),a(n+1)]
Here is how we get S, starting with 1:
S = 1,144,146,153,156,160,165,176,184,197,274,288,294,315,324,336,352,374, ...
1st dif: 143 2 7 3 4 5 11 8 13 77 14 6 21 9 12 16 22
143 is the smallest integer not yet present and dividing 1144 (=8)
2 is the smallest integer not yet present and dividing 144146 (=72073)
7 is the smallest integer not yet present and dividing 146153 (=20879)
3 is the smallest integer not yet present and dividing 153156 (=51052)
4 is the smallest integer not yet present and dividing 156160 (=39040)
5 is the smallest integer not yet present and dividing 160165 (=32033)
11 is the smallest integer not yet present and dividing 165176 (=15016)
...
---
If we drop the "strictly increasing" constraint, we'll get T (which
is an incredible nightmare to calculate by hand):
T = 1, 144, 43, 134, 108, 9, 6, 4, 158, ...
1st dif: 143 101 91 26 99 3 2 154 ...
More terms for S & T (if of interest)?
Best,
É.
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