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
150-159 160-169 170-179
180-inf
Number of sequences
2
68
4
0
0
0
0 0 0
0
 

Statistics about the 74 sequences from 1464 to 9852 as of September 6, 2013


Min
Mean
Max
Index
681
1932.85
7486
Size
151
165.27
189

Size
1-99
100-109
110-119 120-129 130-139
140-149
150-159
160-169
170-179
180-inf
Number of sequences
0
0
0
0
0
0
28
31
12
3



Milestones related to the 74 sequences from 1464 to 9852


August 23, 2013 : The mean size of the terms passed beyond 165 digits.

February 19, 2013 : The smallest term has reached 150 digits (thanks to Tom Womack).
August 21, 2012 : The mean index passed beyond 1900.
July 27, 2012 : The mean size of the terms passed beyond 160 digits.
May 2, 2012 : The mean index passed beyond 1850.

April 22, 2012 : Serge Batalov acquired the downdriver on sequence 345324 which eventually merged with sequence 3366 (345324:i2790 = 3366:i2 = 5940).

February 18, 2012 : The 2^9 * 3 * 11 * 31 driver has been captured on sequence 7044. This is the first time this rare driver appears on an aliquot sequence of leading term < 10,000.

February 18, 2012 : The lowest index has reached 650.
February 15, 2012 : The mean index passed beyond 1800.
December 14, 2011 : The smallest term has reached 140 digits (thanks to Tom Womack).
November 11, 2011 : The mean size of the terms passed beyond 155 digits.

November 6, 2011 :
The largest term has reached 180 digits. (Tom Womack on sequence 8352)

October 22, 2011 : The smallest term has reached 135 digits.
October 22, 2011 : The mean index passed beyond 1750.

March 25, 2011 : The Mersenne Forum team acquired the downdriver on sequence 4788 at height 175 digits. This is a new record for the height of a downdriver capture.

February 24, 2011 : The mean size of the terms passed beyond 150 digits.
February 6, 2011 : The smallest term has reached 130 digits.
November 8, 2010 : The lowest index has reached 600 (thanks to Tom Womack).
October 4, 2010 : The mean index passed beyond 1700.
October 3, 2010 : The mean size of the terms passed beyond 145 digits.
March 24, 2010 : The mean size of the terms passed beyond 140 digits.
November 14, 2009 : The mean index passed beyond 1650.
November 13, 2009 : The largest term has reached 170 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.

September 20, 2009 : The largest term has reached 165 digits. (Mersenne Forum on sequence 4788)
March 5, 2009 : The mean size of the terms passed beyond 135 digits.
December 1, 2008 : The mean index passed beyond 1600.
December 2, 2007 : The mean size of the terms passed beyond 130 digits.

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.

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 !)

August 30, 2006 : The smallest term has reached 120 digits.
July 18, 2006 : The largest index passed beyond 7000.
June 12, 2006 : The mean size of the terms passed beyond 125 digits.
June 9, 2006 : The mean index passed beyond 1500.
May 20, 2006 : The largest term has reached 160 digits.
May 14, 2006 : The largest index passed beyond 6000.

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.

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.

January 23, 2006 : The mean index passed beyond 1450.
January 13, 2006 : The largest term has reached 155 digits.
December 21, 2005 : The largest term has reached 150 digits.
October 22, 2005 : The mean size of the terms passed beyond 120 digits.
October 3, 2005 : The smallest term has reached 110 digits.
September 22, 2005 : The mean index passed beyond 1400.
August 11, 2005 : The mean index passed beyond 1350.
June 29, 2005 : The mean size of the terms passed beyond 115.
May 7, 2005 : The largest term has reached 145 digits.
April 23, 2005 : The largest term has reached 140 digits.
April 4, 2005 : The largest term has reached 135 digits.
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.
February 20, 2005  :  The mean index passed beyond 1300.

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).

January 24, 2005  :  The largest index passed beyond 5700.
January 14, 2005  :  The largest term has reached 130 digits (thanks to Don Leclair).
January 14, 2005  :  The lowest index has reached 500 (thanks to Don Leclair).
January 5, 2005  :  The smallest term has reached 105 digits.
January 3, 2005  :  The largest term has reached 125 digits.
November 24, 2004  :  The mean size of the terms passed beyond 110.
November 16, 2004  :  The mean index passed beyond 1250.
November 16, 2004  :  Half of the sequences have reached 110 digits or more.
September 28, 2004  :  The largest term has reached 120 digits.



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
Benoît Feix
Chad Davis
Dennis Langdeau
Greg Childers
Karsten Bonath
Mersenne Forum
Walter Krickau
Jean-Luc Garambois
Bill Winslow


Contact : christophe.clavier@free.fr 

Last updated : September 6, 2013