|
| |
|
|
A217974
|
|
The ZEBRA Sequence.
|
|
0
|
|
|
|
26, 5, 2, 18, 1, 24, 1, 0, 13, 6, 24, 6, 0, 12, 11, 24, 11, 0, 6, 12, 24, 12, 0, 5, 18, 24, 18, 0, 7, 19, 24, 19, 0, 11, 17, 24, 17, 0, 8, 13, 24, 13, 0, 9, 16, 24, 16, 0, 4, 15, 24, 15, 0, 12, 20, 24, 20, 0, 3, 12, 24, 12, 0, 17, 21, 24, 21, 0, 5, 7, 24, 7, 0, 16, 19, 24, 19, 0, 9, 8, 24, 8, 0, 10, 15, 24, 15, 0, 2, 14, 24, 14, 0, 13, 22, 24, 22, 0, 1, 11, 24, 11, 0, 21, 23, 24, 23, 0, 10, 3, 24, 3, 0, 13, 14, 24, 14, 0, 10, 11, 24, 11, 0, 4, 14, 24, 14, 0, 7, 20, 24, 20, 0, 7, 17, 24, 17, 0, 13, 17, 24, 17, 0, 4, 11, 24, 11, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
If a=1, b=2...
Then ZEBRA = 26,5,2,18,1.
Let the 1st, 3rd, 5th, etc. terms of the sequence be "Black" numbers, and the 2nd, 4th, 6th, etc. be "White" numbers.
Using the first 5 terms as a starting point, to calculate the n-th term, one needs to calculate B(n), the n-th black number using B(n) = B(n-1) - B(n-2). If one runs out of Black numbers to calculate, switch over and calculate White numbers, using the formula W(n) = W(n-1) - W(n-2).
There are no negative terms, so if a negative term appears, multiply it by -1.
A pattern begins to appear: in every group of 5 after the first 8 terms, the 5th term = 0, the middle term = 24 and the 2nd term = 4th term.
|
|
|
LINKS
|
|
|
|
FORMULA
|
B(n) = |B(n-1) - B(n-2)|,
W(n) = |W(n-1) - W(n-2)|.
|
|
|
EXAMPLE
|
First 5 terms; 26,5,2,18,1
Black numbers = 26, 2, 1
White numbers = 5, 18
To calculate the 6th term, Use the formula B(n) = B(n-1) - B(n-2)
6th term = 2 - 26 = -24. But there are no negative terms, so 6th term = 24
7th term = 2 - 1 = 1
8th term = 1 - 1 = 0
We can no longer calculate Black numbers, so we switch to calculating White numbers.
9th term = 1st White term - 2nd White term = 5 - 18 = -13 => No negative terms
=> 9th term = 13
10th term = 18 - 24 = -6 => 6
11th term = 24 - 0 = 24
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
