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OEIS FAQ
Contents
- 1 FAQ for the On-Line Encyclopedia of Integer Sequences
- 2 Use
- 3 Searching
- 3.1 Q: How many terms do I need to look up a sequence?
- 3.2 Q: How do I find which sequences cross-reference a particular sequence?
- 3.3 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?
- 3.4 Q: I've heard about the Motzkin numbers, but I don't know the beginning of the sequence, so how can I find them?
- 3.5 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.
- 3.6 Q: How do I find all the sequences that mention my name?
- 3.7 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?
- 3.8 Q: I searched for a sequence where every other term was 0, but there was no match. What did I do wrong?
- 4 Semantics
- 4.1 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?
- 4.2 Q: Where can I find an explanation of all the different keywords, like "core" and "nice"?
- 4.3 Q: What does the "offset" mean?
- 4.4 Q: What does the keyword "more" mean?
- 4.5 Q: What does the keyword "base" mean?
- 4.6 Q: Can you give an example of a "dumb" sequence?
- 4.7 Q: Why are there sequences with keyword "dead"?
- 4.8 Q. In a formula or comment, what does "empirical" mean?
- 5 Submissions
- 5.1 Q: Which sequences should I submit to the OEIS?
- 5.2 Q: If I just make up a definition of a sequence, should I submit it?
- 5.3 Q: What should I do before submitting a new sequence?
- 5.4 Q: How long should I spend on a submission to the OEIS?
- 5.5 Q: How do I upload a .pdf, .png, .jpg, .txt, .html, etc. file to be attached to an entry?
- 5.6 Q: Can I upload a graph or picture to illustrate a sequence?
- 5.7 Q: I am sending in a comment on one of the sequences. Should I send a copy to the SeqFan mailing list?
- 5.8 Q: What kinds of number may appear in a sequence? Can a sequence include numbers that begin with 0?
- 5.9 Q: A comma appeared in the middle of a number in my sequence - why?
- 5.10 Q: Should one specify links to the Index when submitting sequences?
- 5.11 Q: What are some of the reasons why sequences are rejected?
- 5.12 Q: How can I find out if the sequence I submitted was accepted or rejected?
- 5.13 Q: How long can I expect to wait before my submission is accepted or rejected?
- 5.14 Q: Why am I restricted to a small number of submissions?
- 5.15 Q: I reserved an A-number that I no longer need. What should I do?
- 6 Notation
- 6.1 Q: What notation should I use in equations in the comment and formula lines?
- 6.2 Q: Is it OK to use LaTex or Maple notation in equations?
- 6.3 Q: Should I use juxtaposition to denote multiplication, or should I put a "*" or "." between the things being multiplied?
- 6.4 Q: How should I indicate summations?
- 6.5 Q: Should I denote infinity by "oo"?
- 6.6 Q: Can I use non-ASCII characters?
- 6.7 Q: What does "lgdegf" mean in a reply from Superseeker?
- 7 Format
- 7.1 Q: What is the best format to use when sending in more terms for an existing sequence?
- 7.2 Q: Where can I find an explanation of the internal format used in the database? The %I, %S, etc. lines?
- 7.3 Q: I notice that sometimes you give more than three lines of terms for a sequence. What's the story?
- 7.4 Q: What's the preferred way to enumerate array elements to get an OEIS sequence?
- 7.5 Q: How should an array or triangle be included with the submission?
- 7.6 Q: Some of the entries have figures or other files associated with them. What's your policy on this?
- 7.7 Q: Questions concerning decimal expansion of constants.
- 7.8 Q: How is a musical composition converted to a sequence?
- 8 Participation
- 8.1 Q: How many new sequences and comments come in each day? How big is the database?
- 8.2 Q: What can I do to help?
- 8.3 Q: You asked people to help edit sequences with keyword "uned". What exactly do you need done?
- 8.4 Q: I am emailing you a corrected version of a sequence. Should I say "Edited by ...", "Extended by ...", or not sign it at all?
- 8.5 Q: How can one obtain a file of all the sequences (stripped of formatting) for running tests?
- 8.6 Q: Why are there no mirror sites?
- 8.7 Q: Can one subscribe to the comment mail queue?
- 9 Editing
FAQ for the On-Line Encyclopedia of Integer Sequences
Last updated Nov 09 2015
Use
Q: What is the purpose of the OEIS?
A: The main purpose is to allow mathematicians or other scientists to find out if some sequence that turns up in their research has ever been seen before.
If it has, they may find that the problem they're working on has already been solved, or partially solved, by someone else.
Or they may find that the sequence showed up in some other situation, which may show them an unexpected relationship between their problem and something else.
Another purpose is to have an easily accessible database of important, but difficult to compute, sequences.
For example, if you're testing some conjecture about Mersenne primes, you can look up the ones that are known (see A000043), rather than spending years recomputing them.
Q: How do I cite the OEIS in a paper?
A: Click here.
That is a link to a section of the Welcome page, which has a lot more information about the database.
Q: Can you give some examples of successful applications of the OEIS?
A: See the list of papers that have acknowledged help from the database;
also the comments from readers on the last page of the [[<dont>|Demo]] files.
Q: Some advice for new users and new contributors?
A: (From User:Jonathan_Vos_Post, Jun 07 2008)
New OEIS contributors should be strongly encouraged to use the OEIS webcam to see the breadth and variety of those seqs deemed "nice." It is the equivalent of listening to a radio station that plays the greatest classical or jazz or rock songs (and for that auditory matter using the "listen" feature), or walking through a museum of unusually beautiful Mathematics (and, for that visual matter, encouraging the use of the "graph" feature).
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 n-tuples 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: How do I get the terms of a sequence as a list?
A: (From N. J. A. Sloane 00:44, 10 November 2015 (UTC))
1. Click the "list" button next to start of the sequence. The foot of the new page gives the terms in the DATA section as a list.
2. If the sequence has a b-file, you can download the b-file and create the list by hand with an editor (or with awk). If you are using a MAC, an easy way to do this is to open a Terminal window, and then type (to get A000456, say):
curl -s https://oeis.org/A000456/b000456.txt | awk '{ print $2"," }'
and the list will be printed in that window.
If you want to save the list in a file called William, say, so that you can edit it with TextEdit, type this instead:
curl -s https://oeis.org/A000456/b000456.txt | awk '{ print $2"," }' > William
Note that the A-number 000456 has to be typed twice
William will probably need a bit of editing by hand, because there are sometimes blank lines at the end of the b-file, or comments. Also you will probably want to put brackets at the beginning and end of the list.
The following is a simple Unix shell program that does a better job:
#!/bin/sh # Makes Maple code from a b-file if [ "$#" -ne 1 ] then echo "Usage: btoMaple.sh 001234 >William (give a 6-digit number) to convert b-file from entry in OEIS to a Maple list" exit 1 fi stuff=`echo "$1" | sed 's/A//'` l=`echo "$stuff" | awk ' {print(length($1))}'` if [ "$l" -eq 6 ] then curl -s http://oeis.org/A"$stuff"/b"$stuff".txt | sed '/^#/d /^$/d' | awk ' BEGIN { print("b1 := [ \\ ") } { print $2 ", \\" } ' | sed '$s/,../]:/' else echo "Usage: btoMaple.sh 001234 >William (give a 6-digit number) to convert b-file from entry in OEIS to a Maple list" fi
Searching
Q: How many terms do I need to look up a sequence?
A: It depends!
Usually you should enter about 6 terms, starting with the second term.
Leave off the first term or two, because people may disagree about where the sequence begins.
Don't enter too many terms, because you may have more terms than are in the OEIS right now!
But one regular user says:
Don't hesitate to try the OEIS even if you only have a few terms.
For example, the two terms 2, 1729 identify the "taxicab numbers" A011541.
For a better example, the single number 15170835645 identifies uniquely A003825.
For more information about looking up sequences, see the hints file.
Q: How do I find which sequences cross-reference a particular sequence?
A: Look up the A-number as a word (rather than as a sequence number).
For example, to find all the sequences that mention the Narayana-Zidek-Capell numbers A002083, enter A002083 into the search window.
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),
and I was surprised to find that it wasn't there. How come?
A: You probably miscalculated one of the terms! It is there: A000688.
After 35 years most of the basic sequences are in the database now.
When this happens, please recheck your calculations before submitting the sequence.
It is also possible that you have included an initial term that most people don't include
(perhaps starting a number-theoretic sequence at n=0 rather than n=1).
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?
A: (1) Enter Motzkin numbers into the lookup page. Or (2) use the Index to the OEIS.
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.
A: (January 2006: this problem should now be fixed. The following is the old answer to this question, which is still helpful.)
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, and your sequence should be the first one that is listed.
But for common beginnings, like 2, 3, 5, 7 or 2, 3, 5, 8 there are a lot of possible continuations, and you should give more terms if you have them.
Otherwise, try the Index.
Or go to the Welcome page, and download the section of the database containing sequences around the one you are interested in (in the lexicographic order), and then you can browse. But beware, those files are all quite large.
Incidentally, the Fibonacci numbers are A000045.
Q: How do I find all the sequences that mention my name?
A: Enter your name in the search page.
To find just those where your name is on the Author line, enter author:Smith for example.
To find just those where your name is on the Extension line, enter extension:Smith for example.
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?
A: Simply enter author:Smith lattice in the search page.
Q: I searched for a sequence where every other term was 0, but there was no match. What did I do wrong?
A: As the hints page says, if your sequence looks like a 0 b 0 c 0 d 0 e 0 ..., then search for a, b, c, d, e instead
You should also check your sequence with Superseeker, which applies many transformations to your sequence, including trying to identify the even-indexed and odd-indexed terms separately.
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?
A: A description like "n^2 + 1 is prime" means that the sequence gives a list of the values of n such that n^2 + 1 is prime, that is, 1, 2, 4, 6, 10, 14, ... (A005574).
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"?
A: In the page that describes the format used in replies from the database.
Note that the keywords "huge" and "done" are no longer used.
Q: What does the "offset" mean?
A: It tells you the subscript of the first term in the sequence.
Examples:
- The Fibonacci numbers (A000045) are traditionally denoted by F(0) = 0, F(1) = 1, F(2) = 1, F(3) = 2, F(4) = 3, ...
This sequence starts with F(0), so the offset is 0. - The prime numbers (A000040) are prime(1) = 2, prime(2) = 3, prime(3) = 5, ...; and the offset is 1.
- More generally, the convention in the OEIS is that the first entry in a list has index 1 (rather than 0) so the offset for a list is 1.
- A062361 gives the number of triangular regions in a regular n-gon when all the diagonals are drawn.
This only makes sense for n >=3, so the offset is 3. - If the sequence gives the decimal expansion of a constant,
the offset is the number of digits before the decimal point.- For example, the speed of light is 299792458 (m/sec), giving the sequence 2,9,9,7,9,2,4,5,8 (A003678), with offset 9.
- The decimal expansion of Pi, 3.14159265358979..., gives the sequence 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,... (A000796), with offset 1.
- For a number less than 1, the best thing is to give just the sequence of digits after the decimal point,
so that the offset is 0.
E.g. 1/sqrt(2) = 0.7071067811865475... gives the sequence 7,0,7,1,0,6,7,8,1,1,8,6,5,4,7,5,... (A020759), with offset 0. - The precise definition: if the sequence is a,b,c,d,... and the offset is t, then the number is .abcd... * 10^t.
If the number is a.bcd... * 10^t where a is a single digit, then the sequence is a,b,c,d,... with offset t+1. - If the constant is negative, say so, but give the decimal expansion of the absolute value.
- Always give the actual value in a %e line. For example
%e A020759 1/sqrt(2) = 0.7071067811865475...
And don't forget the keyword "cons". - I found and corrected a huge number of wrong offsets for decimal expansions. Probably many more remain.
That's why it is important to give the actual beginning of the decimal expansion in a %e line.
In the internal format for a sequence the offset line (the %O line) contains two numbers.
The first is the offset as just defined.
The second gives the position of first entry greater than or equal to 2 in magnitude in the sequence (or 1 if no such entry exists), starting counting at 1.
The second offset is used to determine the position of the sequence in the lexicographic order in the database.
For further examples, see the "offset" section of the internal format page.
Q: What does the keyword "more" mean?
A: This is a sequence where more terms are needed.
Ideally the entry gives enough terms to fill three lines on your screen, like this:
%S A027614 1,1,3,14,80,468,2268,10224,313632,9849600,21954240,8894136960, %T A027614 105857556480,20609598562560,650835095904000,80028503341516800, %U A027614 5018759207362252800,503681435808239001600,56090762228110443724800
or
%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 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
If 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?
You can set the WebCam to browse the sequences that need extending,
or use the main look-up page to search for keyword:more.
Q: What does the keyword "base" mean?
A: A sequence where the definition depends on which base we are using.
Palindromes (numbers which are unchanged if the order of the digits is reversed, A002113) are a classic example.
Q: Can you give an example of a "dumb" sequence?
A:
- The number of pages in the n-th volume of the Harry Potter series of children's books. (This was actually submitted! It was rejected for many reasons, one of which is that it is not well-defined — English edition or American? Hard-cover or paperback?)
- See also the section on Examples of What Not to Submit on the OEIS Wiki Main Page.
Q: Why are there sequences with keyword "dead"?
A: Usually they indicate a published sequence that was wrong.
The point is that if someone sees the erroneous sequence in a book and looks it up in the OEIS, the entry will point them to the right sequence.
Q. In a formula or comment, what does "empirical" mean?
A. It means that the statement appears to the author to be true, but he or she has no proof.
This has the same meaning as "Conjecture" or "It appears that" or "It seems that" or "It is very likely that", etc.
If you can supply a rigorous proof (or a reference to a place where a proof can be found), please add it right after the statement, and sign your name (just type four tildes).
Submissions
Q: Which sequences should I submit to the OEIS?
A: Any that actually show up in your research.
If you looked up a sequence in the OEIS and were disappointed that it wasn't there, you should probably [[<dont>|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 cross-reference to the correct sequence.
Q: If I just make up a definition of a sequence, should I submit it?
A: Probably not. It's very easy to define new sequences, but most of them are unlikely to be useful to anyone.
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 made-up sequence of great interest.
Q: What should I do before submitting a new sequence?
A: Check for connections with sequences already in the database. For example, plot the sequence (or its log) to check for clues that it could be formed by intertwining two known sequences.
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?
A: After you've computed enough terms to fill 3 lines, or as many terms as you can, you should probably spend at least an hour writing and checking the definition, comments, references, cross-references, etc.
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: How do I upload a .pdf, .png, .jpg, .txt, .html, etc. file to be attached to an entry?
A:
1. Go to https://oeis.org and login in the top right corner
2. Go to the sequence you want to add the document to
3. Click edit / then "I want to upload a supporting file to store with the OEIS and add a link to it" / navigate to file / upload it
4. Edit the link that will be created for you: add a title, change author(s) name if necessary, move link to correct place in alphabetical order
5. Click Save changes / These changes are ready for review by editors
You can upload .txt and .pdf files in this way.
For .html files, use a name like file.html.txt then upload it as above, then edit the link to delete the suffix .txt , then ask one of the bureaucrats to do the same with the file on the server
Q: Can I upload a graph or picture to illustrate a sequence?
A: Certainly, and we are always happy to get these files. Just follow the instructions in the previous paragraph. See A285471 for examples. Note that if the file is too large (over a few megs) you will have to ask one of the administrators to upload it for you. (You may or may not get an error message if the file is too large. Sometimes it is silently curtailed - you should always check that the full file was uploaded.)
Q: I am sending in a comment on one of the sequences. Should I send a copy to the SeqFan mailing list?
A: No, that's not necessary.
Q: What kinds of number may appear in a sequence? Can a sequence include numbers that begin with 0?
A: No! (except for 0 itself)
Numbers in sequences must be positive or negative integers (or 0).
Acceptable numbers are 1, 5, 101, 0, -25, etc.
Unacceptable numbers are: 020, 7.125, 0.725E03, 3/4, 22?, 123...6 6^6^6^6.
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?
A: Because you split a number across two lines!
My formatting programs assume numbers in a submission are separated by commas, spaces or newlines.
If you mouse a sequence into the window, the mouse may introduce newlines, like this:
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?
A: You certainly may if you know what you are doing! There are plenty of examples in the database.
Just include the link in a links window on the submission page.
Here is a typical link, to the index entries dealing with the Goldbach conjecture.
But when you type it, please type "greater than", "less than", and double-quotes as single characters.
Don't type "less than" as "ampersand l t semicolon" as I had to to make this line visible!
<a href="/index/Go#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?
A: Common reasons are:
- sequence is an incorrect version of a sequence already in the database
- sequence is not well defined
- definition of sequence involves an arbitrary but large integer or an arbitrary real parameter
- sequence is too contrived or artificial
- sequence is too short
- sequence contains numbers involving decimal points, up-arrows, or other unacceptable characters (see above)
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:
0, 1, 5, 6, 10, 25, 50, 60, 76, 100, 101, ...
The parameter 20 here is arbitrary. If we replaced it by 38, say, the sequence would change.
Example: digits of n appear in n^2, n^3 and prime(n):
976, 5903, 10513, 68793, 94682, ...
Too contrived!
Example: even numbers that are not the sum of two primes:
2, ...
Too short! Assuming the Goldbach conjecture is true, there are no more terms. On the other hand, there are several legitimate sequences based on the conjecture, e.g. A002372. See also the Index entries for sequences related to Goldbach conjecture.
Example: superfactorials,
1, 4, 6^6^6^6^6^6, 24^24^...^24 (with 24 copies of 24), ...
- contains unacceptable numbers.
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?
A:
- Wait a few days, then use the Lookup page.
- Or, go to the Welcome page, and scroll down to the "Recent additions" section.
Q: How long can I expect to wait before my submission is accepted or rejected?
A:
- Typically a few days, a week or two, or in rare cases a month or two.
- Sequences that meet all our requirements stand a much better chance of being approved quickly. That is, they are
- interesting,
- mathematically well defined,
- written in correct English, and
- conform to the OEIS formatting style
- Sequences that do not meet these requirements and therefore have to be edited naturally take much longer to be approved.
- Remember that all the editing is done by volunteers, that we have very few editors, and that there are usually several hundred submissions waiting to edited.
- If you would like to help with the editing, please contact one of the Editors-in-Chief. See also Section 8 of this web page.
- Note that our submissions process is very much faster than any journal. The journal Nature recently published an article that showed that in even mediocre journals the median time from submission to acceptance or rejection is about 100 days, and for the top journals (and we like to think the OEIS is one of these) the median time is at least 150 days. See Kendall Powell, The waiting game, Nature, Vol. 530, Feb 11 2016, pp. 148-151.
Q: Why am I restricted to a small number of submissions?
A:
- Because it take a while before new contributors become accustomed to the correct format for OEIS submissions, we automatically restrict new contributors to seven submissions at a time. Before we imposed this limit we would find that we had to send the same message (such as "Examples should be placed in the EXAMPLES section", or "Links to web pages go in the LINKS section") a dozen times.
- People whose submissions require a lot of editing (see Section 5.12) are often restricted to three submissions at a time. If you are in this category, particularly if you are a long-timed contributor, you really need to do a better job of preparing your submissions.
- People who are guilty of unacceptable behavior (making drastic changes to an existing sequence, using abusive language to editors, refusing to follow editors' suggestions, etc.) may be blocked from using the OEIS.
Q: I reserved an A-number that I no longer need. What should I do?
A: Log in, go to the sequence, click Edit, then click Edit internal format, replace all the lines by one single line that says %K recycled and click save.
Notation
Q: What notation should I use in equations in the comment and formula lines?
A: Try to use notation that's as close to standard mathematical notation as is possible using ASCII text.
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:
Use: | to mean: |
---|---|
binomial(n,k) | the binomial coefficient n-choose-k |
sigma(n) |
the sum of the divisors of n, A000203(n) |
phi(n) |
the Euler phi (or totient) function of n, A000010(n) |
mu(n) |
the Moebius function of n, A008683(n) |
pi(n) |
the number of primes <= n, A000720(n) |
prime(n) |
the n-th prime, A000040(n) |
omega(n) |
the number of distinct prime divisors of n, A001221(n) |
bigomega(n) |
the number of prime divisors of n, with multiplicity, A001222(n) |
sqrt(x) | the (positive) square root of x |
floor(x) | the largest integer <= x |
ceiling(x) | the smallest integer >= x |
round(x) | the integer closest to x. |
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 cross-references to other sequences to help with the explanations.
Q: Is it OK to use LaTex or Maple notation in equations?
A: No, please don't!
Use notation that can be understood by humans.
Say (1+x)/(1-x) not $\frac{(1+x)}{(1-x)}$.
Say n^2/2 not 1/2n^2.
Say A/(B*C*D) not A/B/C/D
Say sigma not $\sigma$.
Q: Should I use juxtaposition to denote multiplication, or should I put a "*" or "." between the things being multiplied?
A: Either juxtaposition or an asterisk (*) are OK. Don't use a dot to denote multiplication.
Q: How should I indicate summations?
A: There are many acceptable ways to do this.
All of the following examples are OK.
sum_{i=1..n} i^2 + i
sum_i=1..n (i^2+i)
sum_{d|n} 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"?
A: Generally it is better to say "infinity" explicitly (although oo is also widely used).
Q: Can I use non-ASCII characters?
A: No! Don't use non-ASCII characters! They just cause trouble, and the system may ignore a line containing a non-ascii character without warning you. For example, do not use Greek letters (π, Σ), unusual symbols like "not equal to", less-than-or-equal-to or greater-than-or-equal-to (≤,≥), the 3-dot ellipsis character (…), etc.
Q: What does "lgdegf" mean in a reply from Superseeker?
A: It stands for "logarithmic derivative", which is nothing more than the derivative of the log of a function:
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) = 0
So 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?
A: Please put the full sequence (all the terms, not just the new ones) in the first window of the [[<dont>|Contribute new seq. or comment]] web page.
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?
A: See the internal format page.
Q: I notice that sometimes you give more than three lines of terms for a sequence. What's the story?
A: There is no definite limit on the number of terms that are given in the database.
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?
A: In the case of an infinite square array,
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?
A: Put it in the "Example" (or %e) lines.
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 k-th column is an arithmetic progression with difference 2k-1, and the top entry is the hexagonal number k*(2*k-1) (A000384). %C A079297 The n-th row consists of the odd multiples of n from n*1 to n*(2n-1). %D A079297 R. Honsberger, Ingenuity in Math., Random House, 1970, p. 88. %F A079297 a(n,k) = n(2k-1) for 1<=k<=n. n-th 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?
A: As long as the files are not too big and serve a useful purpose they are welcomed.
Examples of such files are:
- a plain text file giving additional terms for an important sequence, when there are too many to fit on the %S, %T, %U lines (e.g. A000019)
- a gif file illustrating the things being enumerated by the initial terms of a sequence (e.g. A003035, A000012)
- a plain text file giving a computer program for producing an important sequence, when this is too big to fit in the %p, %t or %o lines (e.g. A005132)
- a postscript file plotting the initial terms of an important sequence, but only when this shows some unusual features (again see A005132). In general such plots are unnecessary.
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.
The OEIS contains many sequences giving the decimal expansions of important constants.
For example, the decimal expansion of Pi, 3.14159265358979...,
gives the sequence 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,... (A000796), with offset 1.
Q: What does the "offset" mean for a constant?
A: See above.
Q: How do you handle negative numbers?
A: If the constant is negative, say so, but give the decimal expansion of the absolute value.
- Reminder: Always give the actual value of the constant in a %e line. For example
%e A020759 1/sqrt(2) = 0.7071067811865475...
And don't forget the keyword "cons" (don't use "base").
Q: Do you also want the sequence formed by the continued fraction expansion of the constant?
A: Yes! This should be a separate sequence,
with keyword "cofr",
and there should be cross-references (%Y lines) linking the two sequences.
Q: How is a musical composition converted to a sequence?
Q: Suppose I have a specific piece of music in mind that I would like to transform into a sequence, so that the "Listen to a sequence" feature of the OEIS can play it. How exactly is this done? How does one know which sequence terms produce which sounds? And is there a way to listen to a sequence without having to submit it? And, most importantly, should the OEIS even have more musical compositions as sequences?
A1: I strongly advise no. Most compositions are not of any particular mathematical interest. Arbitrary pedestrian encodings from notes-to-numbers like the OEIS employs are commonplace. Adding more encourages flooding the OEIS with yet more useless noise. These sequences contribute no value, and just pollute serious searches with spurious hits.
I can see making one or two exceptions for the purposes of demonstrating the feature, or for melodies that have some extraordinary relevance for the OEIS. But other than that, please, no more.
A2: I would say there has to be a good scientific reason to include a song as a sequence in the OEIS. When we first set up the procedure for converting a sequence to sounds, David Applegate and I (Neil Sloane) made one example as a test case, a proof-of-concept, which is Fuer Elise. We took the main thread of the music, and converted it to A123456 (easy to remember). If you compare the data for the entry with the musical score, you can see what we did. You could also look at Jonathan Middleton's Music Algorithms web site.
One acceptable reason for including a piece of music as a sequence would be if the music is based on mathematical concepts. Some of Bach's music might qualify, although at present we have no sequences based on Bach's compositions. We do have these examples: A056239 (Karl Aage Rasmussen), A004718 (Per Noergaard). Both are well-known contemporary Scandinavian composers who use mathematics in their work.
Participation
Q: How many new sequences and comments come in each day? How big is the database?
A: The number of new sequences arriving has remained fairly constant at about 10000 per year (i.e. 30 a day) for several years.
The number of comments keeps increasing, and at present averages between 30 and 60 a day. Web traffic on all my web pages averages about 600000 page-downloads per month.
The number of sequences in the OEIS is posted on the main Lookup page and is constantly updated. As of January 2006 it was around 120000. As of June 2019 it is around 325000. The database (just the entries for the sequences, not the illustrations) occupies about 400 megabytes.
Q: What can I do to help?
A:
- Look for sequences in papers in the
- LANL e-print archive (in all categories, not just math.),
- Electronic Journal of Combinatorics,
- Seminaire Lotharingien de Combinatoire,
- SIAM Journal on Discrete Math. [unfortunately you or your library need a subscription for this journal] etc. These and many other free electronic resources are listed in the Directory of Open Access Journals and in the Electronic Library / Journals section of EMIS. There are a large number of other journals available on the Web that often contain sequences, but for which you (or your institution) need a subscription. The European Journal of Combinatorics, the Journal of Mathematical Chemistry are just two of dozens that could be listed here. If you have access to a good library, you should be able to search these journals for new sequences or new references for existing sequences.
- Look for sequences with keyword "uned" or "obsc" and edit them!
- Look out for broken links in the OEIS. (Xenu is the best tool for doing this systematically.) When you find a bad link, be a detective and track down the new URL.
- Extend some of the sequences that need more terms: set the WebCam to browse the sequences that need extending,
or use the main look-up page to search for keyword:more. - See the list of future projects.
Q: You asked people to help edit sequences with keyword "uned". What exactly do you need done?
A: It is not easy to give a precise answer.
The best thing would be to look at some well-written 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 [[<dont>|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?
A: If you just added more terms, say something like:
%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.in-berlin.de), Feb 02 2002
If 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*(x-2)*ln(1-x)-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 2002
Reasons for doing this:
- So you get credit for the changes.
- So you can be contacted in case there is an error!
- To indicate that someone else besides the author has looked at the sequence and approved it.
- To indicate that it has been changed on that date.
Q: How can one obtain a file of all the sequences (stripped of formatting) for running tests?
A: Go to the Welcome page, and scroll down. After a while you will see a link to a stripped-down and gzipped version of the database.
Q: Why are there no mirror sites?
A: This is essentially a one-man operation, and it is hard enough to maintain one site.
Q: Can one subscribe to the comment mail queue?
A: Not at present. But unless I am traveling, comments usually get processed within a few days.
Editing
Q: There is a reference I can't locate — Should I delete it?
A: Absolutely not!
If a sequence has a reference to an article or other source, which you cannot fi nd, DO NOT delete it!
The reference could be important for historical reasons.
A copy may turn up with a more diligent seach.
Many libraries have special collections of manuscripts, private papers, etc., an d one day these will all be scanned.
Neil Sloane has a huge collection of documents going back more than fifty years that were the sources for sequences.
Q: How should I repair a broken link?
A:
About fixing bad links, basically what you should do is edit the link, and change the URL to the new version, while retaining all the other information. And at the end you could say something like [Link corrected by four tildes] (four tildes in a row get replaced by your name and a time stamp).
That's when you can find exactly the same aiticle.
But if you can find only an approximate copy, then put [broken link?] after the one that seems broken, and right after it make a link to the newer version, with something like [Probably the same as the above] after it. (In this case you would not sign what you did)
Even if a link appears to be broken, don't delete it. It probably still exists somewhere in web space!
Thanks to all the sequence fans who suggested questions and answers for this page.