In sequence: Neil Sloane is the Samuel Johnson of numbers. Today I want to write about favourite sequences. It is just an ordered list of numbers whose terms can be described. For example, the prime numbers — the numbers that can only be divided by themselves and 1 — form a sequence: 2, 3, 5, 7, 11, 13, 17, 19, 23, … And there is the Fibonacci sequence, for which each term is the sum of the previous two terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … Ok, so far, so predictable. Prime numbers and Fibonacci numbers are well known throughout general culture. But have you ever heard of the Kolakoski sequence?

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In sequence: Neil Sloane is the Samuel Johnson of numbers. Today I want to write about favourite sequences. It is just an ordered list of numbers whose terms can be described. For example, the prime numbers — the numbers that can only be divided by themselves and 1 — form a sequence: 2, 3, 5, 7, 11, 13, 17, 19, 23, … And there is the Fibonacci sequence, for which each term is the sum of the previous two terms: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … Ok, so far, so predictable.

Prime numbers and Fibonacci numbers are well known throughout general culture. But have you ever heard of the Kolakoski sequence?

The sequence only contains 1s and 2s. They appear either in a run of one, or in a run of two. If we start at the beginning of the sequence, then, as illustrated below, the length of the runs recreates the original sequence. The Kolakoski sequence: the length of each run recreates the sequence. In other words, the Kolakoski sequence describes the length of runs in the sequence itself. It is the only sequence that does this except for the same sequence with the initial 1 deleted.

The first entry is about groups and too complicated for discussion here. The OEIS is one of the best-known mathematical databases on the web and this week it is the subject of a conference at Rutgers University , timed to coincide with its 50th birthday and the 75th birthday of its founder Neil Sloane. Sequences superstar Some people collect stamps, some collect fossils but Neil has always collected sequences. In the s he started to write his favourite ones on file cards.

He was only interested in integer sequences, which are those made up of whole numbers and negative numbers and zero. By he had 2, sequences, which were published as a book: A Handbook of Integer Sequences. Today the OEIS approaches an incredible , sequences! Every day mathematicians around the world send Neil new sequences, which are then approved or rejected for inclusion by him and his team of 20 editors-in-chief and associate editors.

The OEIS still grows by about 40 sequences a day. It is a marvellous resource, which gets about nine million hits a month, and it has turned Neil — who was born in Wales, brought up in Australia and has spent his adult life in the USA — into the sequences superstar.

He mentioned a sequence submitted by Jan Ritsema Van Eck in But if the number k has appeared previously in the sequence, then you count the number of terms since the last appearance of k, and that number is the following term.

In more detail: Term 1: The first term is 0 by definition. And so on. And does every number eventually appear? Neil has lost none of his excitement about sequences. This year he has already submitted more than sequences, bringing his total tally to more than 42, And when I come across a sequence I put it in the database.

You can search for sequences by inputting numbers. So if you put in 0, 1, 1, 2, 3, 5 you will get the Fibonacci sequence, as well as more than others that also include these numbers.

Each sequence has its own page, which lists the early terms, and includes comments and references as well as other information. It also gives you the option to plot a graph of the sequence, or listen to it as a piece of music where each number is a note in a scale of eight octaves.

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## A handbook of integer sequences

Personal information is secured with SSL technology. Free Shipping No minimum order. Description This encyclopedia contains more than integer sequences, over half of which have never before been catalogued. Following sequences of particular interest, thereare essays on their origins, uses, and connections to related sequences all cross-referenced. A valuable new feature to this text is the inclusion of a number of interesting diagrams and illustrations related to selected sequences.

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## Encyclopédie en ligne des suites de nombres entiers

In OEIS lexicographic order, they are: Sequence 1: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, A Sequence 2: 2, 3, 5, 7, 11, , , , , , , , , , , , , , , , A Sequence 3: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, , , , , , , A Sequence 4: 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, , , , , A whereas unnormalized lexicographic ordering would order these sequences thus: 3, 5, 4, 1, 2.

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## HANDBOOK OF INTEGER SEQUENCES SLOANE PDF

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## Neil Sloane: the man who loved only integer sequences

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