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Old 2012-04-03, 18:53   #12
firejuggler
 
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Raman, if you really want, i can advance it a few iteration.. But from what i know of you (various post here) , you seem to be able to do it by yourself.
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Old 2012-04-03, 19:54   #13
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Quote:
Originally Posted by Raman View Post
I found out a new confluence for the Aliquot Sequence

Sequence starting value = 3*2[sup]164[/sup]
for merging with the following
Aliquot sequence = 772032
What's most interesting is that the last two lines are remarkably close to each other. They share their 9 most significant decimal digits, out of 111. Amazing.
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Old 2012-04-03, 20:44   #14
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Quote:
Originally Posted by Dubslow View Post
What's most interesting is that the last two lines are remarkably close to each other. They share their 9 most significant decimal digits, out of 111. Amazing.
If a line factors as 2*3*p = 6p, then the next line will be 1+2+3+6+p+2p+3p = 6p+12 which is only 12 bigger. Very small increases are common for the perfect number drivers.
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Old 2012-04-03, 21:31   #15
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Quote:
Originally Posted by 10metreh View Post
If a line factors as 2*3*p = 6p, then the next line will be 1+2+3+6+p+2p+3p = 6p+12 which is only 12 bigger. Very small increases are common for the perfect number drivers.
yeah I just looked up 2*3*5 and it stays with 6*(p+2) sums until it hits 144 = 12^2 at iteration 6. this seems to lead me to the conclusion that xp would lead to (sigma(x)-x)*p+sigma(x) but I might have missed something else important like they must be of the form sigma(x)=y*x or something ( tested and my computer says sigma(x)=y*x , fits every number so far tested, and I tested the broader claim for 90 claiming x=(2*3^2);p=5 and it worked to predict the next line).

Last fiddled with by science_man_88 on 2012-04-03 at 22:00
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Old 2012-04-03, 23:53   #16
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Quote:
Originally Posted by science_man_88 View Post
yeah I just looked up 2*3*5 and it stays with 6*(p+2) sums until it hits 144 = 12^2 at iteration 6. this seems to lead me to the conclusion that xp would lead to (sigma(x)-x)*p+sigma(x) but I might have missed something else important like they must be of the form sigma(x)=y*x or something ( tested and my computer says sigma(x)=y*x , fits every number so far tested, and I tested the broader claim for 90 claiming x=(2*3^2);p=5 and it worked to predict the next line).
xp->(sigma(x)-x)*p+sigma(x)

and

sigma(x)=y*x

leads to:

((y*x)-x)*p+(y*x) = z*x*p+y*x = (z*p+y)*x so if you know the driver/guide controlling it you can factor the lower number z*p+y
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Old 2012-04-04, 04:17   #17
Raman
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Quote:
Originally Posted by firejuggler View Post
Raman, if you really want, i can advance it a few iteration.. But from what i know of you (various post here) , you seem to be able to do it by yourself.
You need not. I replied it within the response to the message from Stargate38

But, you need to reply to the following question

What is being the smallest Aliquot sequence to merge with
the 3*2[sup]164[/sup].i2434 = 1231600?

Whether if it is being 107-10, 1011, 1013
what is being the good software available to find out what the smallest
Aliquot Sequence merging with some of the above mentioned sequence?
at all,

The last, but not the least, what is being special from the number 4198862272
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Old 2012-04-04, 09:02   #18
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Quote:
Originally Posted by Raman View Post
But, you need to reply to the following question

What is being the smallest Aliquot sequence to merge with
the 3*2[sup]164[/sup].i2434 = 1231600?
Rumor has it that it might be 508980, but don't quote me on it.....
Quote:
Whether if it is being 107-10, 1011, 1013
what is being the good software available to find out what the smallest
Aliquot Sequence merging with some of the above mentioned sequence?
at all,
That's two questions, but what's a couple of overages among collegues? There's nothing, in general, that can do that. Version 1.0 of the FactorDb interface would flag sequences that merged and tell you which lower sequence the merge was with, but Syd hasn't added that to the new frontend code (yet).

I found the above merge through the simple expedient of searching all my local .elf files for a prime from your sequence.....a little slow, but elegantly simple.

Greebley has uploaded some files that contain basically everything, look at the latest threads to find info about that....

[Edited to add: There is also a UBASIC program that can check 2 specific sequences to see if they merge, but it doesn't seem to be on Wolfgang's page right now and Clifford's site is down (gone?)]
Quote:
The last, but not the least, what is being special from the number 4198862272
No idea there, sorry....

Last fiddled with by schickel on 2012-04-04 at 09:07
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Old 2012-04-04, 12:02   #19
Raman
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Quote:
Originally Posted by schickel View Post
Rumor has it that it might be 508980, but don't quote me on it.....
Thanks to you for this, but why not to quote? Are you not being sure that it is being
the smallest? It is certainly being the smallest if it is being
present within the set from the kar_bon's rieselprime.de list; seeing that the smaller number
508980 is available, but that the larger number 772032 is not
at all, at once.

Quote:
Originally Posted by schickel View Post
That's two questions, but what's a couple of overages among collegues? There's nothing, in general, that can do that. Version 1.0 of the FactorDb interface would flag sequences that merged and tell you which lower sequence the merge was with, but Syd hasn't added that to the new frontend code (yet).

I found the above merge through the simple expedient of searching all my local .elf files for a prime from your sequence.....a little slow, but elegantly simple.

Greebley has uploaded some files that contain basically everything, look at the latest threads to find info about that....

[Edited to add: There is also a UBASIC program that can check 2 specific sequences to see if they merge, but it doesn't seem to be on Wolfgang's page right now and Clifford's site is down (gone?)]
If in case that someone wants to test for merges, hereby are being
some more candidates (numbers) to test the merging with, whether.
9999990, 333333 (5400), 3840, 7680, 3152, 9452
888, 828, 990, 2160

Quote:
Originally Posted by schickel View Post
No idea there, sorry....
Okay, alright then
but that the
Can anyone be able to observe thereby guessing the significance from this following sequence?
100, 98.415, 97.2, 95.65938, 94.143178827, 92.98091736, 90.3981141, 90
96 × 1.024 = 98.304 - 98.415 = -0.111 > -1/9; 1.024 = 896/875
53 × 1.024 = 27 => 210 ≈ 103
\frac{128}{125}
293 ≈ 1028 => 265 ≈ 528
\frac{36893488147419103232}{37252902984619140625}
2196 ≈ 1059 => 2137 ≈ 559
\frac{174224571863520493293247799005065324265472}{173472347597680709441192448139190673828125}
2485 ≈ 10146 => 2339 ≈ 5146
\frac{1119872371088902105278721140284222139060822748617324767449994550481895935590080472690438746635803557888}{1121038771459853656738983666631932905024209553501212617405654627111832866148688481189310550689697265625}
22136 ≈ 10643 => 21493 ≈ 5643
213301 ≈ 104004 => 29297 ≈ 54004

Last fiddled with by Raman on 2012-04-04 at 13:02
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Old 2012-04-04, 12:16   #20
schickel
 
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Quote:
Originally Posted by Raman View Post
Thanks to you for this, but why not to quote? Are you not being sure that it is being
the smallest?
This is an American style joke. I can break it down for you if you like.....
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Old 2012-04-04, 16:33   #21
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I interpret it as ' I'm not entirly confident on that'
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Old 2012-04-04, 19:18   #22
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Quote:
Originally Posted by Raman View Post
What is being the smallest Aliquot sequence to merge with the 3*2164.i2434 = 1231600?
Use W.Creyaufmüller's file C9C30:

3*2^164:i2421 = 508980:i3 = 3775104

So 1231600 = 508980:i16

Quote:
Originally Posted by Raman View Post
It is certainly being the smallest if it is being present within the set from the kar_bon's rieselprime.de list; seeing that the smaller number 508980 is available, but that the larger number 772032 is not
My lists of Aliquot sequences on that page are out of date!

Last fiddled with by kar_bon on 2012-04-04 at 19:26
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