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Old 2020-11-23, 22:05   #682
EdH
 
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"Ed Hall"
Dec 2009
Adirondack Mtns

22·13·79 Posts
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Quote:
Originally Posted by VBCurtis View Post
How unusual is it to break 2^4 * 31? I don't think I've done it before tonight.

Edit: The sequence went 2^4 * 3 * 31 to 2^4 * 3 * 31^2 to 2^6 * 3 * 31, and picked up the downdriver a few terms later.
My earlier numbers are probably quite inaccurate! I may need to focus on 2^4 only, rather than 2(>4). I did a bit more study and it appears that 24 * 31 is specifically important! If the power of either 2 or 31 changes, the driver has a really good chance of breaking. There are instances of 2(>4) * 31 and 2^4 * 312 not starting a run.

Example for 10^27 (first column is index number):
Code:
52 = 2^7 * 31 * 37 . . .
170 = 2^5 * 3^2 * 31 * 41 . . .
687 = 2^6 * 3 * 31^2 * 59 . . .
754 = 2^4 * 7 * 31 * 223 . . .
755 = 2^4 * 7 * 31 * . . . 
. . . (2^4 continues for all these lines)
1081 = 2^4 * 3 * 13 * 31 * 2207 . . .
1082 = 2^4 * 3 * 5 * 31 * 47681 . . .
1082 is the current last term, so this instance is unbroken.


Another example 10^111:
Code:
592 = 2^4 * 31 * 73 . . .
593 = 2^4 * 31 * 1493 . . .
. . .
674 = 2^4 * 13 * 31 * 128311 . . .
675 = 2^4 * 5 * 31^2 * 1407503 . . .
676 = 2^4 * 5^2 * 31^2 * 89 . . .
677 = 2^4 * 5^2 * 17 * 31^2 . . .
1087 is the current last term, so this instance broke at 677.

I will do even more study and post something extra later. . .
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