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Old 2012-01-04, 18:36   #1
firejuggler
 
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Default aliquot escape

in this thread we started taking about 'large' perfect driver escape
escape from 2^30*(2^31-1)*x

no escape in less than 20 iteration below x=600000

escape from 2^18*(2^19-1) *x
489885, at i.23 -> end in a prime at i.221=97
538221 at i.22
572127 at i.29
have you found a 'deeper' escape? (more iteration)? have you found 'higher' driver escape?
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Old 2012-01-04, 20:46   #2
Batalov
 
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Phi(4,2^7658614+1)/2

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escape from 2^12*(2^13-1)*k
k=49323 at i50
k=4215 at i76
k=7437 at i77
k=387 at i134

[FONT=Arial Narrow]? M=2^13-1;forstep(k=1,100000,2,k2=k;for(j=1,180,if((k2=2*sigma(k2)-k2)%M==0,if(j>50,print("k="k" at i" j));break)))[/FONT]

escape from 2^16*(2^17-1)*k
k=3045 at i98

escape from 2^18*(2^19-1)*k
k=149235 at i99

Last fiddled with by Batalov on 2012-01-04 at 21:26
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Old 2012-01-04, 21:17   #3
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Quote:
Originally Posted by Batalov View Post
escape from 2^12*(2^13-1)*k
k=49323 at i50
k=4215 at i76
k=7437 at i77
k=387 at i134

[FONT=Arial Narrow]? M=2^13-1;forstep(k=1,100000,2,k2=k;for(j=1,180,if((k2=2*sigma(k2)-k2)%M==0,if(j>50,print("k="k" at i" j));break)))[/FONT]

escape from 2^16*(2^17-1)*k
k=3045 at i98

escape from 2^18*(2^19-1)*k
...
you can make a for loop around it to check multiple M values as well.

Last fiddled with by science_man_88 on 2012-01-04 at 21:17
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Old 2012-01-04, 21:33   #4
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Quote:
Originally Posted by Batalov View Post
escape from 2^12*(2^13-1)*k
k=49323 at i50
k=4215 at i76
k=7437 at i77
k=387 at i134
k=47 at i=247
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Old 2012-01-05, 02:35   #5
Batalov
 
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Quote:
Originally Posted by Batalov View Post
escape from 2^16*(2^17-1)*k
k=3045 at i98
k=5343 at i=240
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Old 2012-01-05, 10:04   #6
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...and k=11367 escapes at i=275
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Old 2012-01-05, 11:45   #7
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... k=4545 at i=276 (same sequence)
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Old 2012-01-05, 12:32   #8
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At the risk of resembling RDS, isn't this a game identical to 'wait for a random number generator to output 131071' ?
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Old 2012-01-05, 13:15   #9
LaurV
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Quote:
Originally Posted by fivemack View Post
At the risk of resembling RDS, isn't this a game identical to 'wait for a random number generator to output 131071' ?
It is more "wait for a kind of number generator to output 131071", but which kind, we don't know, and we try to guess. Everything but random!?!?
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Old 2012-01-05, 13:29   #10
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Quote:
Originally Posted by fivemack View Post
At the risk of resembling RDS, isn't this a game identical to 'wait for a random number generator to output 131071' ?
if doing aliquot sequences ( using sigma) is considered a random number generator ( because the next number isn't known beforehand) then yes it's like that but not a game.
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Old 2012-01-05, 18:52   #11
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Quote:
Originally Posted by fivemack View Post
At the risk of resembling RDS, isn't this a game identical to 'wait for a random number generator to output 131071' ?
Indeed -- and so is the whole aliquot business! :-)
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