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As a biprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot sequence containing only one composite number (21, 11, 1, 0); it is the second composite number with an aliquot sum of 11, following 18. 21 is the first member of the second cluster of consecutive discrete semiprimes (21, 22), where the next such cluster is (33, 34, 35).
To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit. For example: 1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221.
Before PDF version 1.5, the table would always be in a special ASCII format, be marked with the xref keyword, and follow the main body composed of indirect objects. Version 1.5 introduced optional cross-reference streams, which have the form of a standard stream object, possibly with filters applied. Such a stream may be used instead of the ...
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A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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Support for PDF version 1.3; 5.0 May 2001 Last version to support Windows 95 OSR2, Windows 98 First Edition, Windows NT 4.0 Service Pack 5, pre-Service Pack 2 Windows 2000, Mac OS 8.6 and Mac OS 9.0.4 - 9.2.2. Windows, Macintosh, Solaris, HP-UX, AIX, Linux Support for PDF version 1.4; 6.0 July 2003 Adobe Acrobat Reader was renamed to Adobe Reader.
From January 2011 to May 2012, if you bought shares in companies when Donald H. Layton joined the board, and sold them when he left, you would have a -49.6 percent return on your investment, compared to a 4.0 percent return from the S&P 500.