Aliquot sequences that start on the integer powers n^i - Page 15

gd_barnes · 2019-01-19, 07:59

Base 15 all exponents <= 102 is complete to at least size 102, cofactor 97. Highlights:

All odd exponents have terminated.

Merges as previously posted:
15^4, 15^8, 15^18, 15^28, and 15^42

Even exponent terminations as previously posted:
15^6, 15^10, 15^14, and 15^36

Additional termination:
15^22 terminates at term 1375 with P=1361 after reaching 65 digits.

New cycle:
15^74 terminates in a cycle at term 1705 with C=6 after reaching 88 digits.

The base is released.

garambois · 2019-01-19, 17:39

OK, page updated.
Thank you to all !

Bases 15 and 82589933 added.

@gd_barnes :
Bases 14 and 15 released.
I replaced
15^8 term 77 merges with 147150 term 7
by
15^8 term 77 merges with 147150 term 17

My own calculations :
3^232 up to 120 digits.
Poor week for my calculations, only aliquot sequences with drivers like 2^2 * 7 !

gd_barnes · 2019-01-22, 00:00

Some additional work done on base 15:

15^98 had a downdriver at a large size so I continued it. It dropped all the way to 9 digits and so narrowly missed a merge. I added 1048 terms to it. It is now at i=1070, size 106, C97.

15^103 trivially terminated after a short run.

No more work to be done on base 15.

gd_barnes · 2019-01-22, 00:10

I have nominated myself as the "consistency police".

I noticed that all except a few of the bases > 2 have all exponents listed up thru and including the first trivial exponent > 120 digits. Only bases 12, 28, and 439 are missing that final trivial exponent.

Based on this, I trivially terminated the following sequences:
12^112
28^84
439^47

Would it make sense to go ahead and add these to the page? I suggest it because I think it will be interesting to show percentage of exponents terminated/cycled by base in the future to look for patterns. To do this accurately, all bases would need a consistent stopping point.

gd_barnes · 2019-01-24, 19:56

6^113 terminates after reaching 103 digits.

gd_barnes · 2019-01-26, 00:31

I extended many unreserved sequences that did not have drivers -or- had a small cofactor. Several had substantial extensions. Here is a list of the extended sequences:

5^124
6^53
6^83
6^99
6^101
6^113 (Terminated as previously reported!)
6^119
6^123
6^125
7^82
7^88
7^98
7^106
7^116
10^51
10^75
10^89
10^93
10^95
10^97
11^72
12^63
12^69
12^71
12^93
13^42
13^48
13^50
13^78
13^88
14^77
15^44
15^82
15^88

If any more info is needed, let me know.

No reservations.

Most (all) unreserved sequences without drivers should be at >= 105 digits now. :-)

garambois · 2019-01-27, 10:43

OK, page updated.
Thank you to all and especially to gd_barnes.

@gd_barnes :
12^112 added
28^84 added
439^47 added
You're right, it's much cleaner like this !

Congratulations for the non-trivial calculation of 6^113.

My own calculations :
3^210-216-218 up to 120 digits. Last week, it was 3^212 and no 3^232 of course !
And (10^10+19)^15 trivially terminated after a few days.

gd_barnes · 2019-01-28, 08:06

Since the project goal is to search these sequences to 120 digits, I loaded up all remaining unreserved sequences that were at 118 or 119 digits and searched them to >= 120 digits. Here they are:

5^168
5^170
6^151
7^140
11^114
13^104
14^103
15^100

No reservations.

Now you can add a little more color to the page.

ricky · 2019-01-31, 14:21

Hi, I noticed that in sequence 3^108, in factordb, the 1575th term is wrong. Can somebody correct it?

It should be 15540084064757285981320 instead of 15539970862145288285320.

I've written the factordb thread.

firejuggler · 2019-01-31, 17:35

82589933^2 reached 120 digits, 2^2*7 driver, C111
82589933^4 reached 120 digits, 2^4*3, reached 2^8*3^2 during its course, C107
82589933^6 reached 126 digits, 2^3 *3^2, C109
82589933^8 reached 103 digits,2*3 driver
82589933^10 reached 109 digits, 2^5*3*7 , C100
82589933^12 reached 107 digits 2^3*3^3, C101
82589933^14 reached 105 digits, 2*3 driver, C101
82589933^16 reached 122 digits, 2^4 * 3 * 7, C118

relasing 82589933^2 and 82589933^4. Will probably work a few more iteration on 82589933^6, will continue work on others.

gd_barnes · 2019-02-02, 00:10

An extension to my most recent post: I loaded up all remaining unreserved sequences that were at 116 or 117 digits and searched them to >= 120 digits. Here they are:

5^166
6^147
6^149
7^58
7^138
10^115
11^100
11^110
14^99
14^101

All previous size >= 116 sequences are now at size >= 120 digits. (except reserved base 3)

No reservations.

More color for the page.

2019-01-22, 00:00	#157
gd_barnes May 2007 Kansas; USA 3³×5×7×11 Posts	Some additional work done on base 15: 15^98 had a downdriver at a large size so I continued it. It dropped all the way to 9 digits and so narrowly missed a merge. I added 1048 terms to it. It is now at i=1070, size 106, C97. 15^103 trivially terminated after a short run. No more work to be done on base 15. Last fiddled with by gd_barnes on 2019-01-22 at 00:00

2019-01-22, 00:10	#158
gd_barnes May 2007 Kansas; USA 3³·5·7·11 Posts	I have nominated myself as the "consistency police". I noticed that all except a few of the bases > 2 have all exponents listed up thru and including the first trivial exponent > 120 digits. Only bases 12, 28, and 439 are missing that final trivial exponent. Based on this, I trivially terminated the following sequences: 12^112 28^84 439^47 Would it make sense to go ahead and add these to the page? I suggest it because I think it will be interesting to show percentage of exponents terminated/cycled by base in the future to look for patterns. To do this accurately, all bases would need a consistent stopping point. Last fiddled with by gd_barnes on 2019-01-22 at 00:11

2019-01-31, 14:21	#163
ricky May 2018 43 Posts	Hi, I noticed that in sequence 3^108, in factordb, the 1575th term is wrong. Can somebody correct it? It should be 15540084064757285981320 instead of 15539970862145288285320. I've written the factordb thread. Last fiddled with by ricky on 2019-01-31 at 14:48

2019-01-31, 17:35	#164
firejuggler Apr 2010 Over the rainbow 2³×5²×13 Posts	82589933^2 reached 120 digits, 2^27 driver, C111 82589933^4 reached 120 digits, 2^43, reached 2^83^2 during its course, C107 82589933^6 reached 126 digits, 2^3 3^2, C109 82589933^8 reached 103 digits,23 driver 82589933^10 reached 109 digits, 2^537 , C100 82589933^12 reached 107 digits 2^33^3, C101 82589933^14 reached 105 digits, 23 driver, C101 82589933^16 reached 122 digits, 2^4 3 * 7, C118 relasing 82589933^2 and 82589933^4. Will probably work a few more iteration on 82589933^6, will continue work on others. Last fiddled with by firejuggler on 2019-01-31 at 17:36

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2019-01-19, 07:59	#155
gd_barnes May 2007 Kansas; USA 289B₁₆ Posts	Base 15 all exponents <= 102 is complete to at least size 102, cofactor 97. Highlights: All odd exponents have terminated. Merges as previously posted: 15^4, 15^8, 15^18, 15^28, and 15^42 Even exponent terminations as previously posted: 15^6, 15^10, 15^14, and 15^36 Additional termination: 15^22 terminates at term 1375 with P=1361 after reaching 65 digits. New cycle: 15^74 terminates in a cycle at term 1705 with C=6 after reaching 88 digits. The base is released.

2019-01-19, 17:39	#156
garambois "Garambois Jean-Luc" Oct 2011 France 2⁷·5 Posts	OK, page updated. Thank you to all ! Bases 15 and 82589933 added. @gd_barnes : Bases 14 and 15 released. I replaced 15^8 term 77 merges with 147150 term 7 by 15^8 term 77 merges with 147150 term 17 My own calculations : 3^232 up to 120 digits. Poor week for my calculations, only aliquot sequences with drivers like 2^2 * 7 !

2019-01-24, 19:56	#159
gd_barnes May 2007 Kansas; USA 289B₁₆ Posts	6^113 terminates after reaching 103 digits.

2019-01-26, 00:31	#160
gd_barnes May 2007 Kansas; USA 289B₁₆ Posts	I extended many unreserved sequences that did not have drivers -or- had a small cofactor. Several had substantial extensions. Here is a list of the extended sequences: 5^124 6^53 6^83 6^99 6^101 6^113 (Terminated as previously reported!) 6^119 6^123 6^125 7^82 7^88 7^98 7^106 7^116 10^51 10^75 10^89 10^93 10^95 10^97 11^72 12^63 12^69 12^71 12^93 13^42 13^48 13^50 13^78 13^88 14^77 15^44 15^82 15^88 If any more info is needed, let me know. No reservations. Most (all) unreserved sequences without drivers should be at >= 105 digits now. :-)

2019-01-27, 10:43	#161
garambois "Garambois Jean-Luc" Oct 2011 France 2⁷·5 Posts	OK, page updated. Thank you to all and especially to gd_barnes. @gd_barnes : 12^112 added 28^84 added 439^47 added You're right, it's much cleaner like this ! Congratulations for the non-trivial calculation of 6^113. My own calculations : 3^210-216-218 up to 120 digits. Last week, it was 3^212 and no 3^232 of course ! And (10^10+19)^15 trivially terminated after a few days.

2019-01-28, 08:06	#162
gd_barnes May 2007 Kansas; USA 3³·5·7·11 Posts	Since the project goal is to search these sequences to 120 digits, I loaded up all remaining unreserved sequences that were at 118 or 119 digits and searched them to >= 120 digits. Here they are: 5^168 5^170 6^151 7^140 11^114 13^104 14^103 15^100 No reservations. Now you can add a little more color to the page.

2019-02-02, 00:10	#165
gd_barnes May 2007 Kansas; USA 10100010011011₂ Posts	An extension to my most recent post: I loaded up all remaining unreserved sequences that were at 116 or 117 digits and searched them to >= 120 digits. Here they are: 5^166 6^147 6^149 7^58 7^138 10^115 11^100 11^110 14^99 14^101 All previous size >= 116 sequences are now at size >= 120 digits. (except reserved base 3) No reservations. More color for the page.