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Style Sheet
Contents
 1 Style sheet for contributors to the OEIS
 2 Format of entries in the OEIS
 3 A typical entry
 4 How many terms do we need?
 5 Signing your name when you contribute to an existing sequence
 6 Email
 7 Spelling and notation
 8 Common mistakes in English
 9 Technical definitions
 10 Sequences with conjectured terms
 11 If you have solved a famous open problem
 12 See also
Style sheet for contributors to the OEIS
Format of entries in the OEIS
Entries in the OEIS have a rigid format. Each entry contains some or all of the following fields.
Anumber
The Anumber is an A followed by six digits (until we reach A999999). Example:
 This is the absolute catalog number of the sequence.
 Some sequences also have a 4digit Mnumber, such as M1459, which is the number they carried in "The Encyclopedia of Integer Sequences" by N. J. A. Sloane and S. Plouffe, Academic Press, San Diego, CA, 1995.
 Some older sequences also have a 4digit Nnumber, such as N0577, which is the number they carried in "A Handbook of Integer Sequences", by N. J. A. Sloane, Academic Press, NY, 1973.
Name
This gives a brief description or definition of the sequence. Example:
 The even numbers.
 In the description, a(n) denotes the nth term of the sequence and n is a typical subscript.
 Example: a(n) = a(n1) + a(n3).
 In some cases however the definition will describe a typical term k in the sequence.
 Example: Numbers k such that k and k+1 have the same number of divisors.
 Use the notation and spelling as described below.
 Avoid vanity: do not name the sequence after yourself (or your family members, your friends, etc.).
 Prefer concise mathematical definitions when possible.
 When submitting a sequence, once a name has been entered, it might be necessary to make small changes, but for a complete change, e.g., if the original sequence was aborted or withdrawn, do not use the same Anumber; please ask for recycling and request a new Anumber.
Data
This field gives the beginning (at least 4 terms) of the sequence. Example:
 1, 1, 1, 2, 3, 5, 9, 32, 56, 144, 320, 1458, 3645, 9477, 25515, 131072, 327680, 1114112
 Ideally this field should give enough terms to fill about three lines on the screen—maybe 260 characters including [decimal] digits, signs, commas and whitespaces (spaces and newlines; DO NOT USE tabs). (In the above example no more terms were known when the sequence was created.)
 The sequence may contain negative integers—if the sequence is known to contain negative integers it should be labeled with the Keyword "sign" (i.e., signed sequence); if the sequence is known NOT to contain negative integers it should be labeled with the Keyword "nonn" (i.e., nonnegative sequence).
 When entering a sequence, you may separate the terms by commas or spaces.
 The entries must be integers—represented with base10 digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
 If the terms are fractions, then the numerators and denominators should be entered as separate sequences, labeled with the Keyword "frac", and with crossreferences connecting the two sequences.
 Only sequences that are welldefined and of general interest should be submitted.
 If every second term is zero (A, 0, B, 0, C, 0, D, 0, E, ...) then normally we omit the zeros and list the sequence as A, B, C, D, E, ...
Offset
The index of the first term of the sequence. For lists, the offset should normally be 1, but sometimes 0 is allowed. See examples. For arrays and triangles, the offset should be the index of the first row.
 There is a second part to the offset after a comma, which is the 1based index of the first term which is greater than 1 in absolute value. If all terms are 1, 0, or 1 the second part should be 1.
 You do not need to add this part; the server will calculate it for you.
Comments
Relevant information that would make the sequence name much too long and interesting side facts that don't fit in the other fields.
 Generally, comments are placed in chronological order, with newer comments placed at the bottom of the field. However (at the discretion of the EditorsinChief), the most important comments will be placed first, even if they are out of chronological order.
 With the exception of comments made by the author at the time the sequence was first submitted, all comments must identify the commenter and the date the comment was made.
 Therefore there is no need to write in the Extensions field "Added a comment."
 The Comments section is a good place to explain the motivation for a sequence, especially when there are no links.
 There are several ways to sign a comment (and all comments not part of the original submission should be signed and dated) (see below):
 The preferred format for signing a short comment is "If n is divisible by 3, so is a(n).  _Alonso del Arte_, Dec 01 2011". That is, the comment is followed by a space, a dash, a space, then the name (in the form of a link), then a comma, a space, and the date. If you type four tilde characters (~~~~), the system will automatically replace them with your username (in the form of a link), a comma, a space, and the date, all in the proper format.
 Short comments can also be written as "Comment from _Alonso del Arte_, Dec 01 2011: If n is divisible by 3, so is a(n)."
 Another possible format for short comments is "From _Alonso del Arte_, Dec 01 2011: If n is divisible by 3, so is a(n)."
 For a comment that extends over several paragraphs, the preferred format is: "Comment from _Alonso del Arte_, Dec 01 2011: (Start)" followed (starting on a new line) by the comments, then "(End)".
 If a comment contains an error, it may be corrected in place. In that case the author of the correction adds his or her signature as in the following example: "a(n) = a(n1) + 2*(n1).  _Henry Bottomley_, Oct 02 2000 [Corrected by _N. J. A. Sloane_, Jul 18 2010]"
References
References to books, journal papers, and other material not found online.
 There are often multiple mentions of an article, in both the References and Links sections. This is perfectly normal and often desirable, for many reasons. Different versions of a paper may have appeared on the arXiv or a home page and also in a journal; a preprint version may have been sent to the OEIS and later changed in the course of publication. References to the OEIS may have appeared in one version and then dropped, or vice versa. Formulas may have changed. Please do NOT delete references or links just because they appear to you to be duplicates!
 Entries should be alphabetized by the last name of the first author listed. For example, there is a book by John Gold and a paper coauthored by Yang Zhang and Sigfrid Aronson as references for a given sequence. The Gold book goes first, then the Zhang & Aronson paper. (Most math papers list authors alphabetically, but if they use a different ordering use it.)
Links
Links to journal papers, preprints, illustrations, web pages, and other material.
 If a paper appears at more than one location, or in several versions, include all the links (within reason)
 Mark broken links "[broken link]" or similar, or replace the URL with an archived version
 Use stable URLs when available
 Entries should be alphabetized by the last name of the alphabetically first author, except that
 Index entries are placed at the end
 The bfile link is placed at the beginning
 When the author is unknown, write "Author?"; when the title is unknown, write "Title?"
 When the author is a named group, use the name of the group: MathOverflow, N. Bourbaki, Wikipedia, etc.
 When a single source has many links they may be combined. (E.g., several MathWorld articles may be combined into a single line if the Links section grows large.)
Formula
Formulas for calculating the nth term of the sequence, generating functions, asymptotics, and so forth.
See section #Spelling and notation for preferred notation of mathematical formulae. In decimal expansions a formula Equals formula is about the constant, not about the decimal digits a(n).
Example
An example of how to find or interpret terms when it is not obvious.
 In the special case of a constant, give the first few digits of the decimal expansion (usually to the width of the line).
 In the special case of a table, give the first few rows (or the topleft corner if a rectangular array).
 Don't give an example that just repeats the definition. The idea is to choose 1 to 3 simple cases, and show your work.
Maple
A Maple program.
 Please sign and date your contribution in a comment, using Maple's endofline comment syntax, " # ~~~~ ". Or you can start with " # Maple program from ~~~~ ".
 Programs should be selfcontained except in rare cases.
 If a program is extremely long, consider submitting it as a link and mentioning it in this field.
Mathematica
A Wolfram Mathematica program. For much more about Mathematica programs, see Style sheet for Mathematica programs.
 Please sign and date your contribution in a comment, using Mathematica's comment syntax, " (* ~~~~ *) ". Or you can start with " (* Mathematica program from ~~~~ *) ".
 Programs should be selfcontained except in rare cases.
 If a program is extremely long, consider submitting it as a link and mentioning it in this field.
 Code in the Wolfram Language belongs in this field even if it is executed via Wolfram Alpha.
 Programs written specifically in the Wolfram Alpha language are strongly discouraged in the OEIS. The reason is that Wolfram Alpha also accepts inputs that are not in the formal Mathematica language. One can ask Wolfram Alpha something like: "sum the squares from 1 to n". The problem is that the interpretation of a query expressed in natural language is difficult, sometimes produces unwanted results, and even when it gives the expected result there is no guarantee that next year the same English sentence will be interpreted in the same way. Since the OEIS is a scientific database, and reproducibility is essential, programs in Wolfram Alpha are discouraged.
Programs
A program in some language other than Maple or Mathematica.
 Please sign and date your contribution in a comment.
 Programs should be selfcontained and copypastable, except in rare cases.
 If a program is extremely long, consider submitting it as a link and mentioning it in this field like so:

(PARI) \\ See Smith link.
using the appropriate symbol for comments

 Also give the name of the programming language in parentheses at the beginning, like (PARI) or (Perl)
 Entries are generally chronological, but keep entries written in a given programming language together.
Code should be signed unless it was written by the sequence author as part of the original submission. To allow the program to run in case the signature is copied, the signature should be in a comment. The preferred formats for such comments (in languages frequently used in the OEIS), where the block ~~~~
will be automatically replaced by the user's name and the current date, are:
Signature  Languages 

# ~~~~

GAP, Julia, Maple, Perl, Python, R, Ruby, Sage 
/* ~~~~ */

C, Maxima, Rexx 
// ~~~~

C++, Magma, MuPAD 
(* ~~~~ *)

Mathematica 
' ~~~~

Basic 
c ~~~~

Fortran (with the "c" at the start of a line) 
 ~~~~

Haskell 
% ~~~~

MATLAB (with the "%" at the start of a line) 
\\ ~~~~

PARI 
It is no longer necessary to replace leading spaces with dots, for languages that require indentation: as soon as a line starts with two spaces or more, they will be preserved.
Note that code in the Wolfram Language belongs in the Mathematica section, not here, regardless of whether it is executed in Mathematica or Wolfram Alpha, and that code in the Maple language belongs in the Maple section.
Crossreferences
Crossreferences to related sequences. This should be a commaseparated list of sequence numbers without repetition, with a space after each comma.
 You can give extra information, like "Row sums: A000000, A000000, A000000" or "Subsequence of A000000"
 When there is no special information to convey, begin the line "Cf. "
Keywords
One or more of a fixed set of standardized keywords. For more information, see the official descriptions of keywords, clearcut examples of keywords, or an essay on keywords (advanced).
Author
The author's name and the date of initial submission. Sequences with multiple authors should have multiple names here. This field generally does not change once the sequence is first approved.
Older sequences may also include the author's email address; when possible, the author's name should be linked instead.
This field generally represents the person submitting the sequence, even if the sequence was known earlier. For example A000040, the prime numbers, were known long before they were entered in the OEIS, but the author is still listed as N. J. A. Sloane.
Extensions
This field is to claim credit for additions to the entry that can't be properly acknowledged in other fields. The most common use is to acknowledge more terms for sequences that had only a few previously, e.g., "a(10)a(24) from _Jan Schuster_, Mar 14 2015".
 Comments, programs (including Maple and Mathematica), and formulas should be signed (see more about signing above and in QandA) and thus do not need to be mentioned in this field.
 Crossreferences, links, references, and (usually) examples are neither acknowledged in this field nor signed in place.
 During the approval process, you do not need to add anything in this field when making changes to the sequence you are creating.
Status
A noneditable field that shows the status of the sequence: approved, editing, reviewed, or proposed.
 When a sequence is edited, the status is automatically changed to "editing"
 When the status is changed from "editing" to "proposed", the sequence is shown to the Editorial Board for review and approval
 Change this by clicking "These changes are ready for review by an OEIS Editor" at the bottom of the sequence draft
A typical entry
Here is an (abbreviated) example showing the different types of lines in an entry in the OEIS:
 The first line you see has two or three parts:
 A000002 Kolakoski sequence: a(n) is length of nth run; a(1) = 1; sequence consists just of 1's and 2's. ID M0190 N0070
(history; published version; edit) No proposed changes to A000002.
NAME Kolakoski sequence: a(n) is length of nth run; a(1) = 1; sequence consists just of 1's and 2's. DATA 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2 OFFSET 1,2 COMMENTS It is an unsolved problem to show that the density of 1's is equal to 1/2. The sequence is cubefree and all square subwords have lengths which are one of 2, 4, 6, 18 and 54. This is a fractal sequence: replace each run with its length and recover the original sequence.  Kerry Mitchell, Dec 08 2005 ... REFERENCES J.P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 337. E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 3235, Volume 59 (Jeux math'), April/June 2008, Paris. F. M. Dekking, On the structure of selfgenerating sequences, Seminar on Number Theory, 19801981 (Talence, 19801981), Exp. No. 31, 6 pp., Univ. Bordeaux I, Talence, 1981. Math. Rev. 83e:10075. ... LINKS N. J. A. Sloane, <a href="/A000002/b000002.txt">Table of n, a(n) for n = 1..10502</a> J.P. Allouche, M. Baake, J. Cassaigns and D. Damanik, <a href="http://www.lri.fr/~allouche/">Palindrome complexity</a> Michael Baake and Bernd Sing, <a href="http://arXiv.org/abs/math.MG/0206098">Kolakoski(3,1) is a (deformed) model set</a> ... FORMULA These two formulae define completely the sequence: a(1)=1, a(2)=2, a(a(1)+a(2)+...+a(k))=(3+(1)^k)/2 and a(a(1)+a(2)+...+a(k)+1)=(3(1)^k)/2.  Benoit Cloitre, Oct 06 2003 a(n+2)*a(n+1)*a(n)/2 = a(n+2)+a(n+1)+a(n)3 (this formula doesn't define the sequence, it is just a consequence of definition).  Benoit Cloitre, Nov 17 2003 a(n+1)=3a(n)+(a(n)a(n1))*(a(b(n))1), where b(n) is the sequence A156253.  JeanMarc Fedou and Gabriele Fici, Mar 18 2010 EXAMPLE Start with a(1) = 1, a(2) = 2. The rule says that the first run (which is a single 1) has length 1, which it does and the second run (which starts with the 2) has length 2, so the third term must be a 2 also and the fourth term can't be a 2, so must be a 1. So we have a(3) = 2, a(4) = 1. Since a(3) = 2, the third run has length 2, so we deduce a(5) = 1, a(6) = 2. And so on. The correction I made was to change a(4) to a(5) and a(5) to a(6).  Labos Elemer, corrected by Graeme McRae MAPLE M := 100; s := [ 1, 2, 2 ]; for n from 3 to M do for i from 1 to s[ n ] do s := [ op(s), 1+((n1)mod 2) ]; od: od: s; A000002 := n>s[n]; MATHEMATICA a[steps_] := Module[{a = {1, 2, 2}}, Do[a = Append[a, 1 + Mod[(n  1), 2]], {n, 3, steps}, {i, a[[n]]}]; a] PROG (PARI) a=[ 1, 2, 2 ]; for(n=3, 80, for(i=1, a[ n ], a=concat(a, 1+((n1)%2)))); a (PARI) a(n)=local(an, m); if(n<1, 0, an=[1, 2, 2]; m=3; while(length(an)<n, an=concat(an, vector(an[m], i, (m1)%2+1)); m++); an[n]) CROSSREFS Cf. A064353, A001462, A001083, A006928, A042942, A069864, A010060, A078880. Cf. A079729, A079730, A078929, A171899. KEYWORD nonn,core,easy,nice,new AUTHOR N. J. A. Sloane EXTENSIONS arXiv URL replaced with a noncached version by R. J. Mathar, Oct 07 2009 STATUS approved
How many terms do we need?
 Normally an entry in the OEIS will give enough terms to fill three lines on the screen, about 260 characters including spaces and commas. (Enough to fill three punched cards, in the old days.)
 260 characters is just a guide. If you want to give more, go ahead. We are not traffic cops with our radar guns set to flash red at 261 characters. There is ample space. Try to stay under 500 chars, though.
 If more terms are available, then the entry may have a bfile, giving the first 1000 or 10000 or 20000 terms, or more in exceptional cases. The most common size is 10000 terms. The EditorsinChief have the final say about what size of bfile is appropriate.
 If the entry already has about three lines' worth of terms, there is usually no point in adding more terms to the DATA lines  instead, create a bfile.
 Generally, the minimum number of terms required is 4.
Signing your name when you contribute to an existing sequence
 You should sign (i.e., add your name & date) when you add something to an existing entry. This is done by appending
 ~~~~
at the end of the line, which will take care of correctly formatting your name (including the link) and the date. The same information is available in the History section, but it is the standard convention in the OEIS and useful for the reader who does not want to search the history of revisions.  If you are adding something that extends over several paragraphs, then rather than putting your name on every line, put
Comment from _N. J. A. Sloane_, Sep 24 2007: (Start)
at the beginning and(End)
at the end.
T(k,n) = n(k2)((k2)n^2+1+2n)/2.  _R. J. Mathar_, Jun 12 2008 
Comment from _Paul D. Hanna_, Jun 14 2009: (Start) More generally, if G(x) = exp(p*x*exp(q*x*G(x))), where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!, then g(n,m) = Sum_{k=0..n} C(n,k)*p^k*q^(nk)*m*(nk+m)^(k1)*k^(nk). (End) 
T(k,n) = n(k2)((k2)n^2+1+2n)/2. [_R. J. Mathar_, Jun 12 2008] 
Don't include your email address
 Since January 2011, it has been the policy of the OEIS not to display email addresses of contributors.
 Instead, sign your name by typing four tildes (~~~~) at the end of a line to link to your User Page. This should be automatically converted to your name and date at the Preview stage.
 In comments, examples and formulae, this signature is typically preceded by "  " (space, dash, space), separating it from the (mandatory) period (".") at the end of the comment. (Example: "This is a comment.  ~~~~".) But " [~~~~] " is also acceptable (the signature is inserted between square brackets). In programs, the name and date is either put inside comment delimiters (e.g., "(*...*)" in Mathematica), or (preferably) after a commentuptoendofline introducing character or characters, if available ("#" in Maple, "\\" in PARI/GP, "//" in C; see above for other programming languages; this allows users to copy/paste the code and a possibly incomplete part of the signature without generating errors when the code is executed).
 See above for examples.
Sending email to an author or editor
 Provided this person has a user page on this Wiki (and ideally every contributor should have such a page), first go to the OEIS Wiki and log in, then go to the user's page (enter, for example, User:John Doe, in the Wiki search box). Then there should be a link in the Toolbox on the left saying "Email this user". Of course, there are many possible reasons why a contributor, even one with a user page, may not have a current email address.
 You may also leave a message for the user on her or his User Talk page (but again you must first log in to the OEIS Wiki — the Wiki requires a separate login from the main OEIS database).
Spelling and notation
The following are the correct spellings for some words and symbols that are commonly mistyped in the OEIS, also the preferred versions of various useful symbols:
 > (not grth)
 >= (not ≥ or \ge or \geq)
 <= (not ≤ or \le or \leq)
 != or <> for "not equal" (not ≠, .NE., \ne, \neq), e.g., x != y or x <> y.
 For / write a/(bc), not a/b*c or a/b/c which are ambiguous (see operator precedence). For example, don't say 1/6x, say x/6 or (1/6)x. Don't say 1/6 Sum ..., say (1/6) Sum ... . Don't say 1/(1x)/(1x^2), say 1/((1x)(1x^2)).
 S, #S, or card(S) are all acceptable for the cardinality of a set S
 + (not +/ or ±)
 0th, 1st, 2nd, 3rd, 4th, ... (not 0th, 1st, 2nd, 3rd, 4th, ...)
 9gon, not nonagon: numerals are used for figurate numbers above 8
 a(n) for nth term in sequence (not a[n] or a_n)
 a(n) denotes a single term in the sequence. To refer to the whole sequence, use any of {a(n)}, [a(n)], or (a(n)). Of course curly brackets as in P = {2,3,5,7,11,...} usually refer to a set. When you need to distinguish between a sequence and the set of its terms, you need to spell out what you are doing in words. Say something like "Here [a(n): n >= 0] is the sequence, and {a(n)} is the set of its terms."
 behavior (not behaviour  the OEIS uses US spelling)
 billion, trillion, ... (10^9, 10^12, ...) (American system, in which the prefix stands for n in 10^(3+3n))
 binomial(n,k) or C(n,k) for binomial coefficients; the former is preferred but the latter is acceptable in formulas if there are quite a few coefficients. Capitalize "Binomial" only at the beginning of sentence
 cancellation (not cancelation) is the correct spelling
 ceiling (not ceil; not Ceiling, unless at the beginning of a sentence)
 color (not colour  the OEIS uses US spelling)
 cos(x) (not Cos[x])
 cubefree (not cubefree, not cube free)
 dependent (not dependant)
 dissectable (not dissectible)
 e for 2.718281828459... (not E)
 exponentiation: use ^ rather than **, ², or ³.
 Fibonacci (not fibonacci)
 floor (not Floor, unless at the beginning of a sentence). Floor(x) is often denoted by [x].
 Gamma (not GAMMA), for the Gamma function.
 GCD (not g.c.d. or G.C.D.; not hcf or h.c.f. or HCF or H.C.F.): we prefer either GCD or gcd.
 generalize (not generalise  the OEIS uses US spelling)
 groups: The OEIS uses the modern names for groups, as in the ATLAS of Finite Groups and the International Tables for Crystallography. In particular, the dihedral group of order 2n is denoted by D_{2n}. (The old name was D_n.)
 HCF, see GCD
 i, not I, for , the imaginary unit. You can always add 'where i is the imaginary unit' to ensure nobody mistakes it for a summation index.
 iff is a perfectly acceptable abbreviation for "if and only if"
 Im, not im, for imaginary part of a complex number
 independent (not independant)
 infinity (not Inf, inf), but oo is allowed, especially in formulas
 Integral_{x=1..2} f(x) dx or Integral_{x=0..oo} f(x) dx
 The Iverson bracket is very useful in formulas: if P is some property or condition, [P] = 1 if P is true, [P] = 0 if P is false. So you can say "+ 6*[n == 0 (mod 3)] where [] is the Iverson bracket" as a shorthand for "except you have to add 6 if n is a multiple of 3".
 J. S. Bach (not J.S. Bach  a period should be followed by a space, except in hyphenated names like J.P. Serre)
 l (el): try to avoid l in formulas, in many fonts it looks exactly like 1 (one) or I (capital i). Use k or m instead.
 labeled, labeling (not labelled, labelling  the OEIS uses US spelling)
 LCM (not l.c.m. or L.C.M.): we prefer either LCM or lcm.
 lim_{n>P} for limit (use Limit_{n>P} at start of a sentence)
 log_2(x) for logs to base 2
 log(n) (not ln(x) or Log[x]) for logs to base e
 log_10(x) for logs to base 10
 < (not lrth)
 <= (not \le or \leq)
 multiplication sign: use * rather than X, ·, a period (dot), or ×. Both 6n^2+17n+1 and 6*n^2+17*n+1 are acceptable.
 n X n (not n x n, not nXn, not n by n, not nbyn)
 nth, mth, ith, jth, etc. (not nth, mth, ith, jth)
 neighbor (not neighbour  the OEIS uses US spelling)
 nilpotent (not nilpotent)
 noncomposite (not noncomposite)
 nondecreasing (not nondecreasing)
 nonempty (not nonempty)
 nonincreasing (not nonincreasing)
 nonnegative (not nonnegative)
 nonpositive (not nonpositive)
 nonprime (not nonprime)
 nonsquare (not nonsquare)
 nonsquarefree (not nonsquarefree)
 nontrivial (not nontrivial)
 nonunit (not nonunit)
 nonzero (not nonzero)
 occurring (not occuring or ocurring)
 octagon, not 8gon: prefixes are used for figurate numbers below 9
 p(n) should be prime(n) A000040, partition(n) A000041, or something unrelated
 partition(n) is A000041(n), and better than p(n)
 Phi(n,x) for cyclotomic polynomials
 phi for the golden ratio (sometimes tau), phi(n) for the Euler totient function A000010
 Pi for 3.141592653... (not pi)
 prime(n) is the nth prime A000040(n), and better than p(n)
 prime(n) (preferred), or p(n), is usually the nth prime, but both prime(n) and p(n) are also used in other ways
 primeindexed prime (not primeindex prime)
 Product_{k=a..b} for product notation (always use capital "P"), e.g., Product_{k=1..n} a(k)
 proved (not proven)
 Re, not re, for the real part of a complex number
 recurrence (not recurence or reccurrence)
 recurring (not recuring or reccurring)
 semiprime (not semiprime)
 sin(x) (not Sin[x])
 spaces: follow the end of a sentence with one space or two, either way is acceptable
 sqrt(x) (not Sqrt[x] or √x)
 squarefree (not squarefree)
 submatrix (not submatrix)
 Sum_{k=a..b} for summation notation (always use capital "S"), e.g., Sum_{n>0} a(n)
 Sum_{i=1..n} Sum_{j=1..i} f(i,j,n) for a double sum
 tetranacci (not Tetranacci)
 triangular (not Triangular, unless at the beginning of a sentence)
 tribonacci (not Tribonacci)
 zeroth (not zeroeth)
 zeros (not zeroes)
 zeta (for lower case zeta, as in Riemann zetafunction): use zeta not Zeta
NonASCII characters
Don't use nonASCII characters! They just cause trouble, and the system may ignore a line containing a nonASCII character without warning you. For example, do not use Greek letters (π, Σ), unusual symbols like notequalto (≠), lessthanorequalto (≤), greaterthanorequalto (≥), the 3dot ellipsis character (…), etc.
Exceptions: titles of published works and names of authors, OEIS contributors, places, institutions, etc. whose proper spelling requires nonASCII characters; for example:
 "Geneviève Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004."
 A033308 Decimal expansion of CopelandErdős constant: concatenate primes. (Links section: Mikołaj Morzy, Tomasz Kajdanowicz, Przemysław Kazienko, ...)
Grammar
The possessive of a singular noun is formed by adding an apostrophe and an S, even if the noun ends in S. Write "Lucas's theorem", not "Lucas' theorem" (or perhaps "the Lucas theorem"). This rule is not universally accepted, so when directly quoting material for which the original editor did not abide by it, the quotation should not be altered.
Common mistakes in English
 Using a(n) to refer to the whole sequence. That's wrong, a(n) is the nth term.
 To refer to the full sequence, use {a(n)} or the Anumber, such as A123456.
 "allows to" should be changed to "allows us to" or "allows one to"
 "amount" (referring to a number) should be "number"
 WRONG: "The amount of primes in ..."
 CORRECT: "The number of primes in ..."
 CORRECT: "The amount of butter in the cake ..."
 WRONG: "The amount of eggs in the cake ..."
 CORRECT: "The number of eggs in the cake ..."
 "be integer" is wrong.
 WRONG: "Let k be integer"
 CORRECT: "Let k be an integer"
 "couples" instead of "pairs"
 WRONG: "a(n) is the number of couples of binary matrices..."
 CORRECT: "a(n) is the number of pairs of binary matrices..."
 "counts the number of" is wrong. Unless you are working in a hardware store, you don't count numbers.
 WRONG: "a(n) counts the number of ..."
 CORRECT: "a(n) is the number of ..."
 CORRECT: "a(n) gives the number of ..."
 "Except a(5) = 91, ..." is wrong
 WRONG: "Except a(5) = 91, all terms are ..."
 CORRECT: "Except for a(5) = 91, all terms are ..."
 WRONG: "Except the number 2 ..."
 CORRECT: "Except for the number 2 ..."
 "fulfills" is almost always wrong: the correct English word is "satisfies". For some reason, this error is very common among French and German speakers.
 "greater or equal" is wrong
 WRONG: "greater or equal to n"
 WRONG: "greater or equal n"
 CORRECT: "greater than or equal to n"
 CORRECT: ">= n"
 "its" versus "it's":
 "Its", no apostrophe, is the possessive of the pronoun "it": "the sequence is new, and its author is J. Smith"
 "It's", with an apostrophe, is short for "it is" or "it has": "the sequence is new, but it's wrong"
 "less or equal" is wrong
 WRONG: "less or equal to n"
 WRONG: "less or equal n"
 CORRECT: "less than or equal to n"
 CORRECT: "<= n"
 "respectfully" when you should have said "respectively":
 WRONG! "The terms congruent to 0, 1, 2 (mod 3) are respectfully given by A000001, A000002, A000003"
 CORRECT: "The terms congruent to 0, 1, 2 (mod 3) are respectively given by A000001, A000002, A000003"
 CORRECT: "The terms congruent to 0, 1, 2 (mod 3) are given by A000001, A000002, A000003, respectively"
 "triplets" when you should have said "triples"
 WRONG: "a(n) is the number of triplets of binary matrices..."
 CORRECT: "a(n) is the number of triples of binary matrices..."
 Similarly, "quadruple" is preferred over "quadruplet", and so on.
 "unique" when you should have said "distinct"
 WRONG: The list "Tom, Tom, Mary, John" contains three unique names"
 CORRECT: The list "Tom, Tom, Mary, John" contains three distinct names"
Technical definitions
 Divisors  often a source of confusion!
 divisors: numbers d in the range 1 <= d <= n which divide n (A000005, A000203)
 aliquot divisors, aliquot parts: numbers d < n which divide n (see A032741, A001065)
 proper divisors, nontrivial divisors: officially these terms refer to divisors d of n with 1 < d < n (A070824), but are often used incorrectly for divisors d of n with 1 <= d < n (A032741, A001065). You should always specify which definition you are using.
 prime divisors vs. divisors: a common mistake is to say "divisor" when you mean "prime divisor" or even "prime factor".
(Prime factors may occur with multiplicity, while divisors may include p, p^2, ... but not the same p twice: prime divisors is a synonym for prime factors without repetition.)  omega(n) and Omega(n): omega(n) is the number of distinct primes dividing n (A001221), whereas Omega(n) or bigomega(n) counts them with multiplicity (A001222)
 What does "mod n" mean? Many contributors to the OEIS find this confusing.
 a == b (mod c) means that ab is a multiple of c (one reads this as "a is congruent to b mod c"). So 12 == 8 (mod 2).
 a mod c = b means that the remainder when a is divided by c is b. So 12 mod 2 is 0.
Sequences with conjectured terms
In principle, the terms shown in an OEIS entry should have been proved to be correct and complete as far as they are shown. For example, in the list of Mersenne primes, A000043, we don't include terms which are known to be in the sequence if it is possible that there are earlier terms which have not yet been found (although such terms are mentioned in the Comments or Extensions sections).
What do we do when there are terms in a sequence which are only conjectural?
 The most common situation occurs when we know a certain number of terms, but we have only conjectures for the next few terms. In this case we give the terms that are certain in the Data section and the conjectured terms in the Comments or Extensions. This is the rule that we use to handle most cases. Example: A000952, numbers n == 2 (mod 4) for which a conference matrix of order n exists. It is only a conjecture that the next term is 66.
 More than enough terms are known to fill three lines in the Data section, but there are gaps further along in the sequence. In this case we give the known terms (up to the first gap) in a bfile, and all the terms  with gaps, question marks, or ranges for the uncertain terms  in an afile. Example: A072942, which has both a bfile and an afile. A046057 is a sequence from group theory which has an afile although we don't know enough terms for certain to give a bfile.
 We only know a few terms for certain, but there is a conjectured generating function (which may or may not be correct). In this case we sometimes give two sequences, one for the known values and one for the sequence produced by the generating function. Example: A008368, arising from the facecentered cubic lattice, and A023054, from the proposed generating function.
 An extreme example is the sequence of Riesel numbers, A076337, in which only the first term (509203) is known for certain. This violates all our rules, but is included in the OEIS because it is an important problem in number theory, and in the hope that having an entry for it in the OEIS will one day lead to the computation of further terms. The most likely extension is given by A101036. We hope that one day it will be possible to merge the two entries.
 Two further extreme examples: If we were to insist on giving only terms which are known for certain, neither sequence would exist. Because of the importance of these problems, we have made exceptions and relaxed the rules.
 The Brier numbers, A076335. Seven terms are known, but it is only a conjecture that they are the first seven terms. Even the first term shown is only conjectured to be the smallest.
 The minimal number of polygonal pieces needed for dissecting a regular polygon with n sides into an equilateral triangle of the same area: A110000. This is a lovely problem, but only the trivial term a(3)=1 is known for certain. The other terms listed are just upper bounds. Again we hope that including this sequence in the OEIS will lead to the computation of further terms.
 A000373 is a different kind of example. Here there is an explicit formula for a(n), and we can compute as many terms as we wish, but it is only a conjecture that this is the answer to a question of Yuri Manin about Moufang loops.
 Probable primes. We take the point of view that that numbers which at present are known only to be probable primes will eventually be shown to be primes, so we don't regard sequences involving such numbers as conjectural. For example, see A004061, numbers n such that (5^n1)/4 is prime. Whenever possible, you should nonetheless mention which terms only correspond to probable primes.
 See also the entry in the Index to the OEIS for conjectured sequences.
If you have solved a famous open problem
such as Goldbach's conjecture, the 3x+1 conjecture, etc., the OEIS is not the place to publish it. First publish your proof in a (reputable) mathematics journal.
See also
Name · Data · Offset · Comments · References · Links · Formula · Example · Maple · Mathematica · Prog · Crossrefs · Keyword · Author · Extensions 