• The magic number: 1729
• This month's poll: Result and analytic
• About the OEIS.
• Writer and Subscription
1729 is the natural number following 1728 and preceding 1730. It is known as the Hardy–Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation:
I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
The two different ways are:
The quotation is sometimes expressed using the term "positive cubes", since allowing negative perfect cubes (the cube of a negative integer) gives the smallest solution as 91 (which is a divisor of 1729):
Numbers that are the smallest number that can be expressed as the sum of two cubes in n distinct ways have been dubbed "taxicab numbers". The number was also found in one of Ramanujan's notebooks dated years before the incident, and was noted by Frénicle de Bessy in 1657. A commemorative plaque now appears at the site of the Hardy-Ramanujan incident, 2 Colinette Road, Putney.
The same expression defines 1729 as the first in the sequence of "Fermat near misses" (sequence A050794 in the OEIS) defined, in reference to Fermat's Last Theorem, as numbers of the form which are also expressible as the sum of two other cubes.
Edited by Mathematic publication office
Result: 2 votes for 0 digits (don't know what π is), 1 vote for 1-3 digits, 5 votes for 3-5 digits, 5 votes for 5-10 digits, 2 votes for 10-20 digits, 1 vote for 20-25 digits, 1 vote for 25-50 digits and 1 vote for 50-100 digits.
Analytic: 3-5 is one of the most popular votes because they are the digits of π learn in school. 5-10 has the same votes because there are 8 digits and 10 digits appear in most calculator.
(PS: Inven say that he only recited 51 digits, so don't amaze him for recited too much digits of π.)
From next month, we will write about a sequence in OEIS. Here is the introduction:
Most people use the OEIS to get information about a particular number sequence. The sequence database was begun by Neil J. A. Sloane (henceforth, "NJAS") in early 1964 when he was a graduate student at Cornell University in Ithaca, NY. He had encountered a sequence of numbers while working on his dissertation, namely 1, 8, 78, 944, ... (now entry A000435 in the OEIS), and was looking for a formula for the n-th term, in order to determine the rate of growth of the terms.
He noticed that although several books in the Cornell library contained sequences somewhat similar to this, this particular sequence was not mentioned. In order to keep track of the sequences in these books, NJAS started recording them on file cards, which he sorted into lexicographic order.
Here is a scan of the page in NJAS's thesis notebook with the very first collection of sequences. (The sequences mentioned are A000027, A000217, A000292, A000332, A000389, A000579, A000110, A007318, A000058, A000215, A000289, A000324, A234953 (= A001854(n)/n), A000435, A000169, A000142, A000272, A000312, A000111.) This is the acorn from which the OEIS grew. The date is January or February, 1964.
The sequences were transferred to punched cards in 1967, and were made into a book in 1973 ("A Handbook of Integer Sequences", by NJAS, Academic Press, NY). This book contained 2372 sequences.
[Incidentally, today these cards are sometimes referred to as "punch cards" (sic). This is wrong, they were always called "punched cards". Anyone who says "punch cards" is showing they know nothing about the subject. Saying "punch cards" is like saying "hike boots" or "walk stick" or "chew gum".]
NJAS joined AT&T Bell Laboratories in 1969. Following the publication of the book, a large amount of correspondence ensued, with suggestions for further sequences and updates to the existing entries. Many people remarked how useful they found the book, and how surprising it was that no one had published such a collection before.
By the early 1990's over a cubic meter of correspondence had accumulated. A Canadian mathematician, Simon Plouffe, offered to help in preparing a revised edition of the book, and in 1995 "The Encyclopedia of Integer Sequences", by NJAS and Simon Plouffe, was published by Academic Press, San Diego. It contained 5487 sequences, occupying 587 pages. (Incidentally, Simon Plouffe is now one of the Trustees of The OEIS Foundation Inc..)
Again, once the book appeared, many further sequences and updates were submitted from people all over the world. NJAS waited a year, until the size of the collection had doubled, to 10000 entries, and then in 1996 he launched The On-Line Encyclopedia of Integer Sequences® (OEIS®) on the Internet. From 1996 until October 26, 2009, this was part of NJAS's home page on the AT&T Labs website.
During this period, from 1996 to 2009, the database grew by at least 10000 entries per year (18000 new sequences were added in 2009 alone). If it were to be published in book form today, the OEIS would require over 750 volumes, each the size of the 1995 book.
Starting in 2002, NJAS added a group of associate editors to help process submissions. However, because they did not have access to the computer where the database was maintained, almost all the work of updating had to be done single-handedly by NJAS. This involves processing 100 or 200 emails every day, and was getting to be beyond what one person can handle.
In 2009, therefore, it was decided to make a drastic change. NJAS set up a non-profit foundation, The OEIS Foundation Inc., whose purpose is to own, maintain and raise funds to support The On-Line Encyclopedia of Integer Sequences® (OEIS®). On October 26, 2009, NJAS transferred the intellectual property of The On-Line Encyclopedia of Integer Sequences to the Foundation and work was begun on moving the database from NJAS's home page at AT&T to a commercial hosting service.
Here, however, we ran into a very serious problem. In the summer of 2009, when we tried to get the OEIS working as a wiki, we discovered that the Mediawiki software was not capable of handling the kind of queries that arise in looking up sequences. This was a disaster.
It took us over a year to resolve this problem. In the end, Russ Cox completely rewrote all the programs needed to maintain the database and answer queries - a huge task! NJAS's colleague David Applegate has also been of enormous help in getting the new system working. As a result of their work, the new OEIS was finally launched on November 11, 2010. It is now possible for anyone in the world to propose a new sequence or an update to an existing sequence. To do this, users must first register. A group of about 130 editors has been formed, whose job it is to review submissions before they become a permanent part of the OEIS.
So, after nearly two years of struggle, the OEIS was finally able to operate without NJAS having to approve every change. After 46 years of running the database, this came as a great relief to him.