- #1
ramsey2879
- 841
- 3
Bench Top's thread revived a number string curiosity that once stumped me. I wonder if anyone else saw anything like this before and can give the sequence a name.
Description
1. The sequence comprises only numbers from 1 to 2n.
2. Each number from 1 to 2n appears once and only once.
3. For i = 1 to n, the 2i(th) number minus the 2i-1(th) number is i.
examples
a)for n = 1 the sequence is <1,2>
b)there are no valid sequences for n = 2 or 3
c)for n = 4 one valid sequence and its cousin is <2,3,6,8,4,7,1,5>/<6,7,1,3,2,5,4,8>. The cousin of a sequence is found by letting each 2i-1(th) number of the new sequence be equal to 2n +1 minus the 2i(th) number of the first sequence.
There are sequences for even larger n but they are not readily available to me.
The questions which stumped me are:
1. Is there a rule for which values n can take?
2. Is there an algorithm for determining a valid sequence?
3. Is there a rule for determining how many valid sequences there are for a given n?
Does anyone have any thoughts on this?
Description
1. The sequence comprises only numbers from 1 to 2n.
2. Each number from 1 to 2n appears once and only once.
3. For i = 1 to n, the 2i(th) number minus the 2i-1(th) number is i.
examples
a)for n = 1 the sequence is <1,2>
b)there are no valid sequences for n = 2 or 3
c)for n = 4 one valid sequence and its cousin is <2,3,6,8,4,7,1,5>/<6,7,1,3,2,5,4,8>. The cousin of a sequence is found by letting each 2i-1(th) number of the new sequence be equal to 2n +1 minus the 2i(th) number of the first sequence.
There are sequences for even larger n but they are not readily available to me.
The questions which stumped me are:
1. Is there a rule for which values n can take?
2. Is there an algorithm for determining a valid sequence?
3. Is there a rule for determining how many valid sequences there are for a given n?
Does anyone have any thoughts on this?