## Web--of-- Ones polynomials derived(1)

Expand Messages
• Begin with a quadratic equation whose solutions have prime factors limited to integers ending in 1,5 or 9 such as x^2 + x -1, generating the sequence
Message 1 of 1 , Mar 18, 2006
Begin with a quadratic equation whose solutions have prime factors
limited to integers ending in 1,5 or 9 such as x^2 + x -1,
generating the sequence 1,5,11,19,29,41,55,71,89,109,131,155...
Find a sub sequence whose members all end in one such as
5 * (11,31,61,101,151) : five are sufficient to generate the rest
using difference equations. With the square version of the
ancient form of Ulam's spiral produce a partial grid such as :

3251 3001 2761 2531 2311
1361 1201 1051 911 2101
451 361 281 781 1901
101 61 211 661 1711
11 31 151 551 1531

Check all of the diagonals left to right, bottom to top,
for prime factors that
end with a nine within twenty or so terms and eliminate them from
consideration; We are left with two sequences, both of which
are good candidates for inclusion in the Web-of Ones:
11, 61, 281, 911, 2311... and
31, 211,781 2101, 4651....
From the central diagonal check the rows and columns similarly,
11, 101, 451, 1361 3251 looks good. There may be more usable
sequences in the extended grid. A rule analagous to a primality
test to checkthese sequences without actually factoring all
of its members is needed, because such a task is impossible.
Your message has been successfully submitted and would be delivered to recipients shortly.