Aliquot sequences
(with leading term <
10,000)
There are other pages related to aliquot sequences, and maintained by:
Note that the seven sequences 276, 552, 564, 660, 966, 1074 and 1134
are pursued by Paul Zimmermann.
Click here to have a status for
these sequences or contact Paul
Zimmermann for obtaining more up-to-date information.
Early 2003, I decided to carry on the work done by Juan L.
Varona and pursue and maintain all other open ending aliquot
sequences with
leader < 10,000. Here are some stats about these sequences at that
time as well as today.
A comprehensive table for all open ending sequences from 1464 to 9852
(with links to sequence files) may be found here. Please contact
me if you want to reserve some sequence,
some factorization or report any result.
Statistics
about the 74 sequences from 1464 to 9852 as of early
2003
|
Min
|
Mean
|
Max
|
Index
|
427
|
1197.12
|
5583
|
Size
|
92
|
103.57
|
111
|
Size
|
1-99
|
100-109
|
110-119
|
120-129 |
130-139
|
140-149
|
150-159 | 160-169 | 170-inf
|
Number
of sequences
|
2
|
68
|
4
|
0
|
0
|
0
|
0 | 0 | 0
|
Statistics
about the 74 sequences from 1464 to 9852 as of January 26, 2010
|
Min
|
Mean
|
Max
|
Index
|
572
|
1657,55
|
7261
|
Size
|
124
|
138,80
|
172
|
Size
|
1-99
|
100-109
|
110-119
|
120-129 |
130-139
|
140-149 |
150-159 | 160-169 | 170-inf
|
Number
of sequences
|
0
|
0
|
0
|
18
|
22
|
28
|
3 | 2 | 1
|
Milestones
related to the 74 sequences from 1464 to 9852
September 28, 2004 : The largest term has reached 120
digits.
November 16, 2004 : Half
of the sequences have reached 110 digits or more.
November 16, 2004 : The
mean index passed beyond 1250.
November 24, 2004 : The
mean size of the terms passed beyond 110.
January 3, 2005 : The
largest term has reached 125 digits.
January 5, 2005 : The
smallest term has reached 105 digits.
January 14, 2005 : The
lowest index has reached 500 (thanks to Don Leclair).
January 14, 2005 : The
largest term has reached 130 digits (thanks to Don Leclair).
January 24, 2005 : The
largest index passed beyond 5700.
February 20, 2005 : Sequence 1578 got the downdriver (2^1 * 3^0
* ...) at index 1185 (110 digits) and decreased up to index 1868
(5 digits) where it reached the value 56,440. Sequence 56,440 which was
unfinished can be removed from tables as it is now linked to sequence
1578. Also, a new record for the greatest descent of an unfinished
sequence has been established (from 111 to 5 digits).
February 20, 2005 : The
mean index passed beyond 1300.
February 22, 2005 : Mark
Hudson got the downdriver on sequence 3678 at index 1396 with 110
digits. Sequence reached a maximum at index 1398 with 111 digits, and
decreased down to 23 digits at index 1868 on March 15, 2005. It
then rapidly raised up to more than 100 digits at index beyond 2600.
April 4, 2005 : The
largest term has reached 135 digits.
April 23, 2005 : The
largest term has reached 140 digits.
May 7, 2005 : The
largest term has reached 145 digits.
June 29, 2005 : The
mean size of the terms passed beyond 115.
August 11, 2005 : The
mean index passed beyond 1350.
September 22, 2005 : The
mean index passed beyond 1400.
October 3, 2005 : The smallest term has reached 110 digits.
October 22, 2005 : The mean size of the terms passed beyond 120 digits.
December
21, 2005 : The largest term has reached 150 digits.
January 13, 2006 : The largest term has reached 155 digits.
January
23, 2006 : The mean index passed beyond 1450.
April 4, 2006 : Sequence
1578 acquired the downdriver at height 132 digits (index 4359). This
establishes a new record for the height of a downdriver capture.
May 2, 2006 :
After having progressed by more than one thousand index in only few
days, sequence
1578 reached index 5760 and thus overtake up-to-then record sequence
8760. Sequence 1578 is now the longest one whose leader is less than
10,000.
May 14, 2006 : The largest index passed beyond 6000.
May 20, 2006 :
The largest term has reached 160 digits.
June 9, 2006 : The
mean index passed beyond 1500.
June 12, 2006 : The mean size of the terms passed beyond 125 digits.
July 18, 2006 : The largest index passed beyond 7000.
August 30, 2006 : The smallest term has reached 120 digits.
November 21,
2006 : Sequence 1578 became the longuest aliquot sequence ever
computed. Previous record was sequence 389508 with index 7135.
(As of January 2008 this is no more a record since sequence 389508 reached index 8000 !)
January
13, 2007 : Benoît Chevallier-Mames acquired the downdriver on
sequence 9684 at height 133 digits (index 1234). This is a new record
for the height of a downdriver capture.
December 2, 2007 : The mean size of the terms passed beyond 130 digits.
December 1, 2008 : The mean index passed beyond 1600.
March 5, 2009 : The mean size of the terms passed beyond 135 digits.
September 20, 2009 : The largest term has reached 165 digits. (Mersenne Forum on sequence 4788)
September 29, 2009 : Sequence
1560 acquired the downdriver at height 142 digits (index 1650). This is a new record for the height of a downdriver capture.
November 13, 2009 : The largest term has reached 170 digits. (Mersenne Forum on sequence 4788)
November 14, 2009 : The mean index passed beyond 1650.
Credits
to contributors to this project
I would like to thank the following persons who contributed to the
sequences since the creation of this page, as well as everyone who
contributed earlier.
Don Leclair
Robert Wilson
Thorsten Kleinjung
Mark Hudson
Chris Monico
Sander Hoogendoorn
Marc Joye
Benoit Chevallier-Mames
Igor Schein
Donovan Johnson
Bernardo Boncompagni
Philippe Strohl
Josh Ball
Frank Schickel
Tom Womack
Benoit Feix
Chad Davis
Dennis Langdeau
Greg Childers
Karsten Bonath
Mersenne Forum
Contact : christophe.clavier@free.fr
Last updated : January 26, 2010