login 
Annual appeal: Please make a donation to keep the OEIS running!
Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate
FAQ for the OnLine Encyclopedia of Integer SequencesFrequently Asked QuestionsLast updated Jun 07 2008. I need to update this page to refer to the new OEIS at oeis.org  N. J. A. Sloane, Jan 15 2011.
ContentsUseQ: What is the purpose of the OEIS?Q: How do I cite the OEIS in a paper? Q: Can you give some examples of successful applications of the OEIS? Q: Some advice for new users and new contributors? Q: OEIS Summer Rules, Jun 02 2008, but still valid today! SearchingQ: How many terms do I need to look up a sequence?Q: How do I find which sequences crossreference a particular sequence? Q: I looked up a really basic sequence (the number of abelian groups of order n, in fact), and I was surprised to find that it wasn't there. How come? Q: I've heard about the Motzkin numbers, but I don't know the beginning of the sequence, so how can I find them? Q: I was trying to find the entry for the Fibonacci numbers, but when I entered 2, 3, 5, 8, 13 I got too many matching sequences. Q: How do I find all the sequences that mention my name? Q: How can I get hold of all the sequences submitted by John Smith that mention "lattice", so I can analyze them on my computer? SemanticsQ: Sometimes a sequence will say "n^2 + 1 is prime", sometimes it says "Primes of the form n^2 + 1". What's the difference?Q: Where can I find an explanation of all the different keywords, like "core" and "nice"? Q: What does the "offset" mean? Q: What does the keyword "more" mean? Q: What does the keyword "base" mean? Q: Can you give an example of a "dumb" sequence? Q: Why are there sequences with keyword "dead"? SubmissionsQ: Which sequences should I submit to the OEIS?Q: If I just make up a definition of a sequence, should I submit it? Q: What should I do before submitting a new sequence? Q: How long should I spend on a submission to the OEIS? Q: What "Subject" line should I use when submitting a new sequence or comment? Q: I am sending in a comment on one of the sequences. Should I send a copy to the SeqFan mailing list? Q: What kinds of number may appear in a sequence? Can a sequence include numbers that begin with 0? Q: A comma appeared in the middle of a number in my sequence  why? Q: Should one specify links to the Index when submitting sequences? Q: What are some of the reasons why sequences are rejected? Q: How can I find out if the sequence I submitted was accepted or rejected? NotationQ: What notation should I use in equations in the comment and formula lines?Q: Is it OK to use LaTex notation in equations? Q: Should I use juxtaposition to denote multiplication, or should I put a "*" or "." between the things being multiplied? Q: How should I indicate summations? Q: Should I denote infinity by "oo"? Q: What does "lgdegf" mean in a reply from Superseeker? FormatQ: What is the best format to use when sending in more terms for an existing sequence?Q: Where can I find an explanation of the internal format used in the database? The %I, %S, etc. lines? Q: I notice that sometimes you give more than three lines of terms for a sequence. What's the story? Q: What's the preferred way to enumerate array elements to get an OEIS sequence? Q: How should an array or triangle be included with the submission? Q: Some of the entries have figures or other files associated with them. What's your policy on this? Q: Questions concerning decimal expansion of constants. ParticipationQ: How many new sequences and comments come in each day? How big is the database?Q: What can I do to help? Q: You asked people to help edit sequences with keyword "uned". What exactly do you need done? Q: I am emailing you a corrected version of a sequence. Should I say "Edited by ...", "Extended by ...", or not sign it at all? Q: How can one obtain a file of all the sequences (stripped of formatting) for running tests? Q: Why are there no mirror sites? Q: Can one subscribe to the comment mail queue?
There is already a lot of information about
the Encyclopedia on other pages,
Use
Q: What is the purpose of the OEIS?
If it has,
they may find that the problem they're working on has already been solved,
or partially solved, by someone else.
Another purpose is to have an easily accessible database of important,
but difficult to compute, sequences.
For more information on this point, see the Demo files and the Welcome page.
Q: How do I cite the OEIS in a paper?
Q: Can you give some examples of successful
applications of the OEIS?
Q: Some advice for new users and new contributors? Another positive message to new OEIS contributors, to enhance that sense of community, and to provide a balance against "making stuff up" without reference to what is known and had been judged interesting, is, beyond looking for duplicates, looking from triples and ntuples of sequences that are implicitly related, and making that relationship explicit, perhaps by showing that these are different rows or columns or diagonals of the same previously unshown array. Or by making the analogy: sequence A is to sequence B as sequence C is to sequence D. Or by using the transforms available on some sequence previously not so transformed. The goal is, not to merely reward ("nice") or punish ("less" or "probation" or silent deletion) those contributors externally, but by enhancing their intrinsic motivation to make a contribution more likely to be appreciated.
Q: OEIS Summer Rules, Jun 02 2008, but still valid today!
Thank you! Neil Sloane
Searching
Q: How many terms do I need to look up a sequence? But one regular user says: Don't hesitate to try the OEIS even if you only have a few terms.For more information about looking up sequences, see the hints file.
Q: How do I find which sequences crossreference
a particular sequence? If you only want to see sequence A002083, enter id:A002083 . You could also enter Narayana Zidek into the search window. For more information about looking up sequences, see the hints file.
Q: I looked up a really basic sequence (the number
of abelian groups of order n, in fact),
When this happens, please recheck your calculations
before submitting the sequence. Of course it is entirely possible that your sequence really isn't in the database, in which case please submit it!
Q: I've heard about the Motzkin numbers,
but I don't know the beginning of the sequence,
so how can I find them? Incidentally, the Motzkin numbers are A001006.
Q: I was trying to find the entry for the Fibonacci numbers,
but when I entered 2, 3, 5, 8, 13 I got too many matching sequences. Use the Index to the OEIS.
If you are in the right ballpark, the replies will be sorted with
the "core" sequences first, followed
by the "nice" sequences,
Or go to the
Welcome page,
and download the section of the database
containing sequences around the one you are
interested in
Incidentally, the Fibonacci numbers are A000045.
Q: How do I find all the sequences that mention my name?
Q: How can I get hold of all the sequences submitted by
John Smith that mention "lattice", so I can analyze
them on my computer?
Semantics
Q: Sometimes a sequence will say
"n^2 + 1 is prime",
sometimes it says
"Primes of the form n^2 + 1".
What's the difference? On the other hand, "Primes of the form n^2 + 1" means that the sequence gives a list of the actual primes, 2, 5, 17, 37, 101, 197, 257, ... (A002496). It is easy to get them confused! (But in this case it is easy to tell the difference: 4 is not a prime.)
Q: Where can I find an explanation of all the different keywords,
like "core" and "nice"? Note that the keywords "huge" and "done" are no longer used.
Q: What does the "offset" mean? Examples:
In the internal format for a sequence the offset line (the %O line)
contains two numbers. For further examples, see the "offset" section of the internal format page.
Q: What does the keyword "more" mean? %S A027614 1,1,3,14,80,468,2268,10224,313632,9849600,21954240,8894136960, %T A027614 105857556480,20609598562560,650835095904000,80028503341516800, %U A027614 5018759207362252800,503681435808239001600,56090762228110443724800or %S A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %T A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, %U A000004 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0If you can extend a sequence which has fewer terms than that, please do so, even if the keyword "more" is missing.
See also
What is the format to use when sending in more terms?
Q: What does the keyword "base" mean?
Q: Can you give an example of a "dumb" sequence?
This was actually submitted! It was rejected for many reasons,
one of which is that it is not welldefined
Q: Why are there sequences with keyword "dead"?
Submissions
Q: Which sequences should I submit to the OEIS? If you looked up a sequence in the OEIS and were disappointed that it wasn't there, you should probably submit it so the next person who looks for it will find it. Also, most sequences that appear in published papers should be in the OEIS. That way, if someone sees a sequence in a paper and looks it up, they'll be able to find out if anything new has been learned about the sequence since the paper was published. Even if a published sequence happens to be wrong, it should be in the OEIS, with a crossreference to the correct sequence.
Q: If I just make up a definition of a sequence,
should I submit it? There are exceptions. If it is a really beautiful sequence, go ahead and submit it! See the EKG sequence (A064413) for an example of a madeup sequence of great interest.
Q: What should I do
before submitting a new sequence? For triangles or tables, check the columns, row sums, skew diagonals etc. to see if they are already in the database. If so, mention this in the submission. Check your sequence with Superseeker Study the first differences of your sequence to see if they provide any clues. Make sure you give the correct offset (see above)! If there is a relation to a geometric or combinatorial problem, describe this: it's valuable information. And finally, if possible, please give a formula!
Q: How long should I spend on a submission to the OEIS? If you don't think the sequence is worth spending an hour of your time on, then it's probably not worth having in the OEIS. Take the time to make sure that everything is accurate and explained clearly, so that someone who hasn't seen the sequence before will understand how it's defined and why it's interesting or important. Include any references that you know about. Remember the advice given in the submit new sequence page:
IMPORTANT: Thousands of people use the sequence database every day. Please take great care that the terms you send are absolutely correct. The standards are those of a mathematics reference work.
Q: What "Subject" line should I use when
submitting a new sequence or comment?
Subject: NEW SEQ for unnumbered new sequences, It makes the editing process easier if there is only one type of comment in a message. That is, please don't mix "Comments" and "New Sequences" (or "Edited Sequences") in a single email!
Q: I am sending in a comment on one of the sequences.
Should I send a copy to the
SeqFan mailing list?
Q: What kinds of number may appear in a sequence? Can a sequence include numbers that begin with 0? But see also the section in the hints file on dealing with fractions and real numbers.
Q: A comma appeared in the middle of a number in my sequence  why?
My formatting programs assume numbers in a submission
are separated by commas, spaces or newlines. 8,12,20,24,32,36,48,52,60,68,80,84,96,100,112,120,128,140,144,152,168,172,19 2,200...That would cause the number 192 to appear as 19,2
Q: Should one specify links to the
Index when submitting sequences?
Here is a typical link, to the index entries dealing
with the Goldbach conjecture. <a href="Sindx_Go.html#Goldbach">Index entries</a> for sequences related to Goldbach conjecture</a>. At some later time you should then send me a list of updates to the index itself.
Q: What are some of the reasons why sequences are rejected?
Example: primes that contain the digits 2003. The "2003" is an arbitrary and large parameter.
Example:
numbers n such that the digits of n appear in all powers n^s with s = 1 through 20:
Example:
digits of n appear in n^2, n^3 and prime(n):
Example: even numbers that are not the sum of two primes:
Example: superfactorials, On the other hand, number sequences that have actually appeared on quizzes or tests are welcomed. One of the reasons for the OEIS's existence is to help people with such tests!
Q: How can I find out if the
sequence I submitted was accepted or rejected?
Notation
Q: What notation should I use in equations in
the comment and formula lines? Don't use notation that's specific to Maple, Mathematica, PARI, or some other computer language, except in %p, %t, or %o lines. In particular, the arguments of functions should be enclosed in parentheses, not brackets; most function names should not be capitalized. Here are some common examples:
In most cases, it's a good idea to explain what function you mean, since some of these function names aren't standardized, or are used for other things. For example, "pi(n+1)" might also mean the number pi multiplied by n+1. Use crossreferences to other sequences to help with the explanations.
Q: Is it OK to use LaTex or Maple notation in equations?
Use notation that can be understood by humans.
Q: Should I use juxtaposition to denote multiplication, or should I put
a "*" or "." between the things being multiplied?
Q: How should I indicate summations? All of the following examples are OK. sum_{i=1..n} i^2 + i sum_i=1..n (i^2+i) sum_{dn} d^3 sum_{ 2 <= p <= n, p prime} p^2 Other styles also acceptable, as long as they are clear!
Q: Should I denote infinity by "oo"?
Q: What does "lgdegf"
mean in a reply from Superseeker?
d log(f(x)) f'(x) lgdegf f(x) =  =  dx f(x) The replies from Superseeker are sometimes hard to read, I admit! For example, suppose it says: SUGGESTION: LISTTOALGEQ FOUND ONE OR MORE ALGEBRAIC EQUATIONS SATISFIED BY THE GEN. FN. WARNING: THESE MAY BE ONLY APPROXIMATIONS! Equation(s) and type(s) are: 2 3 [8  12 a(n) + 6 a(n)  a(n) , lgdegf]What this means is the following. Let f(x) be the generating function for your sequence, and let a(x) be the logarithmic derivative of f(x). Then Superseeker has found that a(x) may satisfy the equation 2 3 8  12 a(x) + 6 a(x)  a(x) = 0So you solve that for a(x), which is f'(x)/f(x), and then try to solve for f(x). Like I said, this takes a bit of getting used to! But it can be very helpful.
Format
Q: What is the best format to use when sending in
more terms for an existing sequence? In the "Comments" window, put something like "More terms". Or if you have found a mistake, say "Corrected and extended". If it is a signed sequence (that is, contains negative numbers), just give the signed version in the top window, and don't bother to include the sequence of absolute values. The updating programs will take care of that.
Q: Where can I find an explanation of the internal format
used in the database? The %I, %S, etc. lines?
Q: I notice that sometimes you give
more than three lines of terms for a sequence.
What's the story? The sequence of numbers of meanders (A005316) for example, is exceptionally long. This is because the sequence is interesting, the terms are fairly difficult to compute, and so it seems worthwhile giving as many as possible. The editing programs will normally truncate the sequence to three lines (roughly 180 to 210 characters including the separating commas, depending on the program), but they can be overruled. If you feel the sequence is important enough to justify this, please add a note to that effect in the Comments. If fewer than three lines worth are given, feel free to compute some more terms!
Q: What's the preferred
way to enumerate array elements to get an OEIS sequence? a11 a12 a13 ... a21 a22 a23 ... a31 a32 a33 ... a41 a42 a43 ... ...............this normally gets read by antidiagonals and recorded as the sequence a11 a12 a21 a13 a22 a31 ... or a11 a21 a12 a31 a22 a13 ... (pick whichever seems nicer  or use both). See A003987 for an example.
Q: How should an array or triangle
be included with the submission? For instance (A079297):
%I A079297 %S A079297 1,2,6,3,9,15,4,12,20,28,5,15,25,35,45,6,18,30,42,54,66,7,21,35,49,63, %T A079297 77,91,8,24,40,56,72,88,104,120,9,27,45,63,81,99,117,135,153,10,30,50, %U A079297 70,90,110,130,150,170,190,11,33,55,77,99,121,143,165,187,209,231,12 %N A079297 Triangle read by rows: the kth column is an arithmetic progression with difference 2k1, and the top entry is the hexagonal number k*(2*k1) (A000384). %C A079297 The nth row consists of the odd multiples of n from n*1 to n*(2n1). %D A079297 R. Honsberger, Ingenuity in Math., Random House, 1970, p. 88. %F A079297 a(n,k) = n(2k1) for 1<=k<=n. nth row adds to n^3. %e A079297 Triangle begins: %e A079297 1 %e A079297 2 6 %e A079297 3 9 15 %e A079297 4 12 20 28 %e A079297 5 15 25 35 45 %e A079297 6 18 30 42 54 66 %K A079297 nonn,tabl,easy %O A079297 1,2 %A A079297 njas, Mar 04 2003
Q: Some of the entries have figures or other
files associated with them. What's your policy on this?
The reason for including these files on the OEIS web site is that it is hoped that this is more permanent than people's individual home pages.
Q: Questions concerning decimal expansion of constants.
For example,
the decimal expansion of Pi, 3.14159265358979...,
Participation
Q: How many new sequences and comments come in each day? How big is the database? The number of sequences in the OEIS is posted on the main Lookup page and is constantly updated. As of January 2006 it is around 120000. The database (just the entries for the sequences, not the illustrations) occupies about 100 megabytes.
Q: What can I do to help?
Q: You asked people to
help edit sequences with keyword "uned". What exactly do you need done? The best thing would be to look at some wellwritten entries in the OEIS (here are some picked at random off the WebCam: A001316, A055545, A052402, A007308). Then look at the two web pages that describe the internal format and the standard or beautified format used in the replies from the lookup service. This is how things should be! Now look at some entries with keyword "uned". (Search here.) Usually you will see that many things are wrong! The description is obscure, or the entries are obviously wrong, or the English is hopeless, etc. To help, make a copy of the sequence in the internal format, edit it (very carefully) and email it to me (njasloane@gmail.com) using subject line "EDITED A012345" (say). Sequences that need a lot of work have keyword "uned", but there many others that could be improved. If you don't see anything wrong, send me email saying sequence A012345 (say) looks fine and doesn't need further editing.
Q: I am emailing you a corrected version of a sequence. Should I say "Edited by ...", "Extended by ...", or not sign it at all? %E A060031 More terms from Larry Reeves (larryr(AT)acm.org), Jan 01 2003 %E A070171 Corrected and extended by Ralf Stephan (ralf(AT)ark.inberlin.de), Feb 02 2002If you made some nontrivial changes, say something like: %E A067581 Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 03 2002 %E A069841 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 04 2002 %F A083741 G.f.: 3*(x2)*ln(1x)5*x+x^2.  Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 06 2003 %F A006721 a(n) is asymptotic to C^n with C=1.226.......  Benoit Cloitre (abcloitre(AT)wanadoo.fr), Aug 07 2002Reasons for doing this:
Q: How can one obtain a file of all the sequences (stripped of formatting) for running tests?
Q: Why are there no mirror sites?
Q: Can one subscribe to the comment mail queue?
Thanks to all the sequence fans who suggested questions and answers for this page.
