[seqfan] Dividing the sum of the k leftmost digits of N by k
Eric Angelini
Eric.Angelini at kntv.be
Wed Aug 26 19:04:21 CEST 2009
Hello SeqFans, [idea coming from the recent 'average' post by Zakir]
is 978015 the biggest number N with no two same digits having the pro-
perty that when the sum of the k leftmost digits of N is divided by k
the result is always an integer?
N = 978015
- dividing the sum of the 2 leftmost digits by 2: (9+7)/2 = 8
- dividing the sum of the 3 leftmost digits by 3: (9+7+8)/3 = 8
- dividing the sum of the 4 leftmost digits by 4: (9+7+8+0)/4 = 6
- dividing the sum of the 5 leftmost digits by 5: (9+7+8+0+1)/5 = 5
- dividing the sum of the 6 leftmost digits by 6: (9+7+8+0+1+5)/6 = 5
Many seq based on this idea could be added to the OEIS (if of interest)
The same with the rightmost digits.
(see http://www.research.att.com/~njas/sequences/A061383
"Arithmetic mean of digits is an integer.")
Best,
É.
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