What are the next several lines and how are they formed?

Do the sequences have any special feature?

Does the pattern continue indefinitely?

prime 2 :  1,1
prime 3 :  1,2,1
prime 5 :  1,3,2,3,1
prime 7 :  1,4,3,2,3,4,1
prime 11: 1,5,4,3,5,2,5,3,4,5,1
prime 13: 1,6,5,4,3,5,2,5,3,4,5,6,1

Every line is the next above line, with as many numbers as necessary so the number of numbers is a prime. So, the next line will have 17 numbers, and we need four numbers "7", placed as the "5" was placed when writing the prime11th-line:

prime17: 1,7,6,5,4,3,5,7,2,7,5,3,4,5,6,7,1 

prime19: 1,8,7,6,5,4,3,5,7,2,7,5,3,4,5,6,7,8,1

prime23: 1,9,8,7,6,5,4,3,5,9,7,9,2,7,5,3,4,5,6,7,8,9,1

That is, when two numbers must be added, they are added in the extremes. When four numbers must be added, the other two are placed in the middle, "enclosing" a single number.

Thatīs the pattern that we can deduce from the given data.

Now that we must add 6 numbers, the first four are:

prime29:1,10,9,8,7,6,5,4,3,5,9,7,10,9,10,2,7,5,3,4,5,6,7,8,9,10,1 

To place the others 2 numbers "10", I think that thereīs no sufficient information from the given data.

Edited on October 31, 2005, 3:10 pm

Edited on October 31, 2005, 3:12 pm

Edited on October 31, 2005, 3:14 pm

Posted by pcbouhid on 2005-10-31 14:58:31