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 uptodate 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

199

100109

110119

120129 
130139

140149

150159 
160169 
170179

180inf

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

199

100109

110119

120129 
130139

140149

150159

160169

170179

180inf

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 ChevallierMames 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 uptothen 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 ChevallierMames
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
JeanLuc Garambois
Bill Winslow
Contact : christophe.clavier@free.fr
Last updated : September 6, 2013