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Old 2007-02-16, 07:08   #34
ATH
Einyen
 
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Dec 2003
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I looked at the LL-sequence without the mod step:
S0=4, S1=14, S2=194, S3=37634, S4=1416317954, S5=2005956546822746114,....

For every p where Mp is a Mersenne prime, Sp-2 is divisible by Mp and by 2 (Sp-2 always even). I found that if you divide Sp-2 by 2*Mp and add 1 to the remaining factor that number is divisible by 2p and the remaining factor is odd. That is:

Sp-2 = 2*Mp*(n*2p - 1)

Where n is the remaining (big) odd factor.

I only tested this for S3, S5, S11, S15, S17, S29 corresponding to M5, M7, M13, M17, M19, M31, so this might be the Law of small numbers . (Allthough S29 isn't exactly "small" at 307,062,002 digits )

Next possible number to test this on is S59 corresponding to M61, but at 3.3*1017 digits that isn't likely.

Last fiddled with by ATH on 2007-02-16 at 07:57
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