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Old 2012-06-24, 23:55   #4
fivemack
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Feb 2006
Cambridge, England

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Here's an analysis over the 115-to-125-digit elements of all the sequences I've run:

a.b.c.d.e means 2^a * 3^b * 5^c * 7^d * 31^e

Numbers in brackets at the beginning are the number of lines I saw with that exponent combination.

The first probability is the chance of going from one exponent-set to another, so a measure of stability.

Numbers in brackets at the end are the average change in log(K) of such lines.

So: powers of three are the annoying ones, the worst driver for making sequences get larger is 2^2*3^2*5, 2^3*3 is beautifully stable and drives terms up fast. Powers of two with no other small primes get less stable as the exponent increases.

Code:
1.0.0.0.0	(564)	0.901 1.0.0.0.0 (-0.245)	
		0.053 1.0.1.0.0 (-0.262)	
		0.023 1.0.0.0.1 (-0.242)	
		
1.0.1.0.0	(99)	0.586 1.0.1.0.0 (-0.054)	
		0.263 1.0.0.0.0 (-0.044)	
		0.111 1.0.2.0.0 (-0.016)	
		
1.1.0.0.0	(433)	0.857 1.1.0.0.0 (0.045)	
		0.046 1.1.1.0.0 (0.041)	
		0.032 1.2.0.0.0 (0.018)	
		
1.1.1.0.0	(69)	0.507 1.1.1.0.0 (0.180)	
		0.304 1.1.0.0.0 (0.171)	
		
1.2.0.0.0	(209)	0.756 1.2.0.0.0 (0.108)	
		0.057 1.1.0.0.0 (0.094)	
		0.057 1.3.0.0.0 (0.101)	
		
1.2.1.0.0	(60)	0.700 1.2.1.0.0 (0.226)	
		0.217 1.2.0.0.0 (0.232)	
		
1.3.0.0.0	(91)	0.692 1.3.0.0.0 (0.132)	
		0.132 1.2.0.0.0 (0.108)	
		
2.0.0.0.0	(2003)	0.846 2.0.0.0.0 (-0.078)	
		0.057 2.0.1.0.0 (-0.082)	
		0.024 2.0.0.0.1 (-0.079)	
		
2.0.0.0.1	(67)	0.776 2.0.0.0.0 (-0.049)	
		
2.0.1.0.0	(414)	0.580 2.0.1.0.0 (0.085)	
		0.280 2.0.0.0.0 (0.078)	
		0.075 2.0.2.0.0 (0.075)	
		0.031 2.0.1.0.1 (0.076)	
		
2.0.2.0.0	(84)	0.321 2.0.2.0.0 (0.124)	
		0.286 2.0.0.0.0 (0.103)	
		0.274 2.0.1.0.0 (0.110)	
		
2.1.0.0.0	(1130)	0.795 2.1.0.0.0 (0.156)	
		0.052 2.0.0.0.0 (0.143)	
		0.045 2.2.0.0.0 (0.140)	
		0.039 2.1.1.0.0 (0.149)	
		0.022 2.1.0.0.1 (0.161)	
		0.019 2.3.0.0.0 (0.149)	
		
2.1.1.0.0	(209)	0.574 2.1.1.0.0 (0.277)	
		0.278 2.1.0.0.0 (0.273)	
		0.096 2.1.2.0.0 (0.273)	
		0.014 2.1.3.0.0	
		0.010 2.1.0.0.1	
		0.010 2.2.1.0.0	
		0.010 2.1.1.0.1	
		0.005 2.1.1.0.2	
		0.005 2.2.0.0.0	
		
2.1.2.0.0	(53)	0.321 2.1.2.0.0 (0.300)	
		0.245 2.1.0.0.0 (0.312)	
		0.226 2.1.1.0.0 (0.294)	
		
2.2.0.0.0	(432)	0.650 2.2.0.0.0 (0.218)	
		0.086 2.1.0.0.0 (0.203)	
		0.049 2.0.0.0.0 (0.195)	
		0.049 2.2.1.0.0 (0.216)	
		0.046 2.3.0.0.0 (0.196)	
		
2.2.1.0.0	(106)	0.500 2.2.1.0.0 (0.339)	
		0.274 2.2.0.0.0 (0.338)	
		
2.3.0.0.0	(130)	0.538 2.3.0.0.0 (0.231)	
		0.154 2.2.0.0.0 (0.220)	
		0.123 2.1.0.0.0 (0.211)	
		
3.0.0.0.0	(975)	0.907 3.0.0.0.0 (-0.014)	
		0.029 3.0.0.0.1 (-0.013)	
		*0.021 2.0.0.0.0* (-0.052)	
		*0.019 4.0.0.0.0* (-0.049)	
		
3.0.1.0.0	(265)	0.879 3.0.1.0.0 (0.130)	
		0.049 3.0.2.0.0 (0.133)	
		
3.0.2.0.0	(58)	0.621 3.0.2.0.0 (0.155)	
		0.293 3.0.1.0.0 (0.154)	
		
3.1.0.0.0	(572)	0.946 3.1.0.0.0 (0.217)	
		0.024 3.1.0.0.1 (0.209)	
		
3.1.1.0.0	(178)	0.888 3.1.1.0.0 (0.331)	
		0.073 3.1.2.0.0 (0.315)	
		
3.2.0.0.0	(179)	0.771 3.2.0.0.0 (0.263)	
		0.067 3.1.0.0.0 (0.274)	
		
3.3.0.0.0	(75)	0.587 3.3.0.0.0 (0.291)	
		0.160 3.2.0.0.0 (0.258)	
		
4.0.0.0.0	(443)	0.767 4.0.0.0.0 (0.018)	
		0.077 4.0.1.0.0 (0.016)	
		*0.027 3.0.0.0.0* (-0.019)	
		
4.0.0.0.1	(129)	0.860 4.0.0.0.1 (0.051)	
		
4.0.1.0.0	(132)	0.583 4.0.1.0.0 (0.160)	
		0.265 4.0.0.0.0 (0.142)	
		
4.1.0.0.0	(216)	0.782 4.1.0.0.0 (0.239)	
		0.060 4.0.0.0.0 (0.208)	
		0.051 4.2.0.0.0 (0.232)	
		
4.1.0.0.1	(109)	0.798 4.1.0.0.1 (0.266)	
		
4.2.0.0.0	(64)	0.625 4.2.0.0.0 (0.299)	
		0.172 4.1.0.0.0 (0.281)	
		
4.2.0.0.1	(53)	0.604 4.2.0.0.1 (0.303)	
		
5.0.0.0.0	(247)	0.745 5.0.0.0.0 (0.054)	
		
5.1.0.0.0	(151)	0.828 5.1.0.0.0 (0.280)	
		0.093 5.1.1.0.0 (0.264)	
		
6.0.0.0.0	(179)	0.721 6.0.0.0.0 (0.036)	
		
6.1.0.0.0	(60)	0.750 6.1.0.0.0 (0.248)
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