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Style sheet for contributors


Contents

Style sheet for contributors to OEIS

Format of entries in OEIS

Entries in the OEIS have a rigid format. Each entry contains some or all of the following fields.

A-number

The A-number is an A followed by six digits (until we reach A999999). Example:

A005132
  • This is the absolute catalog number of the sequence.
  • Some sequences also have a 4-digit M-number, 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 4-digit N-number, 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 n-th term of the sequence and n is a typical subscript.
    Example: a(n) = a(n-1) + a(n-3).
  • In some cases however n denotes a typical term in the sequence.
    Example: Numbers n such that n and n+1 have the same number of divisors.
  • Use standard mathematical notation: a(n) NOT a[n], sqrt not Sqrt, etc.
  • 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been entered, it might be needed to make small changes; but for a complete change, as if the sequence was aborted or withdrawn, it is not possible to use the same A-number; please ask for recycling and request a new A-number.

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 base-10 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 cross-references connecting the two sequences.
  • Only sequences that are well-defined 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. (See examples.) For lists, the offset should be 1 (rather than 0).

  • There is a second part to the offset after a comma, which is the 1-based 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 Editors-in-Chief), 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):
    • 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 dash, then name (in the form of a link), then the date. The system will do that for you if you type a dash followed by four tildes.
    • For a comment that extends over several lines, the preferred format is: "Comment from _Alonso del Arte_, Dec 01 2011 (Start)" followed by the comments, then (End)
    • 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)."

References

References to books, journal papers, and other material not found online.

  • If a book or paper is available online, the bibliographic information should appear under the link (so there is only one entry).
  • 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 co-authored 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 b-file 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.)
  • Usually, you should not add a b-file until the sequence has been approved (except for example if you are confident that the sequence will be approved)

Formula

Formulas for calculating the n-th term of the sequence, generating functions, asymptotics, and so forth.

See section #Spelling_and_notation for preferred notation of mathematical formulae.

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 top-left 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 end-of-line comment syntax, " # ~~~~ ". Or you can start with " # Maple program from ~~~~ ".
  • Programs should be self-contained 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 self-contained 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 from some other language.

  • Please sign and date your contribution in a comment.
  • Programs should be self-contained 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.
  • Also give the name of the programming language in parentheses at the beginning, like (PARI) or (Perl)
  • Entries are generally chronological, but keep 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 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) are:

  • Basic: ' ~~~~
  • C: /* ~~~~ */
  • C++: // ~~~~
  • Fortran: c ~~~~ (with the "c" at the start of a line)
  • Haskell: -- ~~~~
  • Magma: // ~~~~
  • Maple: # ~~~~ (but this belongs in the Maple section)
  • Mathematica: (* ~~~~ *) (but this belongs in the Mathematica section)
  • Matlab:  % ~~~~ (with the "%" at the start of a line)
  • Maxima: /* ~~~~ */
  • MuPad: // ~~~~
  • Pari: \\ ~~~~
  • Python: # ~~~~
  • R: # ~~~~
  • Ruby: # ~~~~
  • Sage: # ~~~~

For Python and Sage programs, leading spaces should be replaced by dots (i.e., periods). The following sed command, which was written by Paul Staniforth, converts leading spaces into dots:

sed -e ':again' -e 's/^\( *\)[ ]\([^ ]\)/\1.\2/; t again' program.py

The following sed command will convert the leading dots back into spaces:

sed -e ':again' -e 's/^\(\.*\)[.]\([^.]\)/\1 \2/; t again' program_with_leading_dots.py

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.

Cross-references

Cross-references to related sequences. This should be a comma-separated list of sequence numbers without repetition.

  • 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, clear-cut 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 and thus do not need to be mentioned in this field
  • Cross-references, links, references, and (usually) examples are neither signed nor acknowledged in this field
  • During the approval process, you do not need to add anything in this field when doing changes to the sequence you are creating.

Status

A non-editable 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 n-th 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 n-th 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 by its length and recover the original sequence. - Kerry Mitchell (lkmitch(AT)gmail.com), 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. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.

F. M. Dekking, On the structure of self-generating sequences, Seminar on Number Theory, 1980-1981 (Talence, 1980-1981), 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)=3-a(n)+[a(n)-a(n-1)]*[a(b(n))-1], where b(n) is the sequence A156253. - Jean-Marc 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+((n-1)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+((n-1)%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, (m-1)%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 non-cached 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.)
  • If more terms are available, then the entry may have a b-file, giving the first 1000 or 10000 terms, or more in exceptional cases.
  • 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 b-file.
  • 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 on 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 lines, then rather than putting your name on every line, put "From _N. J. A. Sloane_, Sep 24 2007: (Start)" at the beginning and "(End)" at the end.
  • Example 1: The fraction of 0's in the first n terms approaches 1/phi (see for example Allouche and Shallit). - _N. J. A. Sloane_, Sep 24 2007
  • Example 2: T(k,n) = n(k-2)((k-2)n^2+1+2n)/2. - _R. J. Mathar_, Jun 12 2008
  • Example 3:
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^(n-k)*m*(n-k+m)^(k-1)*k^(n-k).
(End)
  • Example 4: T(k,n) = n(k-2)((k-2)n^2+1+2n)/2. [_R. J. Mathar_, Jun 12 2008]

Email

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 comment-up-to-end-of-line introducing character or characters, if available ("#" in Maple, "\\" in PARI/GP, "//" in C; see above for other programming languages) [which allows users to copy-paste the code and a possibly incomplete part of the signature].
  • 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), 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 "E-mail 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.

Spelling and notation

The following are the correct spellings for some words and symbols that are commonly mistyped in the OEIS:

  • > (not grth)
  • >= (not \ge or \geq)
  • /: 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/(1-x)/(1-x^2), say 1/((1-x)(1-x^2)).
  • 0th, 1st, 2nd, 3rd, 4th, ... (not 0-th, 1-st, 2-nd, 3-rd, 4-th, ...)
  • 9-gon, not nonagon: numerals are used for figurate numbers above 8
  • a(n) for n-th term in sequence (not a[n] or a_n)
  • 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
  • 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])
  • 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)
  • GCD (not gcd or g.c.d. or G.C.D.; not hcf or h.c.f. or HCF or H.C.F.), except in mathematical formulae, where "gcd" is preferred
  • generalize (not generalise)
  • HCF, see GCD
  • i, not I, for \sqrt{-1}, the imaginary unit. You can always add 'where i is the imaginary unit' to ensure nobody starts to look for a definition of some summation index.
  • independent (not independant)
  • J. S. Bach (not J.S. Bach - a period should be followed by a space, except in hyphenated names like J.-P. Serre)
  • LCM (not lcm or l.c.m. or L.C.M.), except in mathematical formulae, where "lcm" is preferred
  • lim_{n->P} for limit (use Lim_{} 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, ·, 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)
  • n-th, m-th, i-th, j-th, etc. (not nth, mth, ith, jth)
  • neighbor (not neighbour - the OEIS uses US spelling)
  • nilpotent (not nil-potent)
  • noncomposite (not non-composite)
  • nondecreasing (not non-decreasing)
  • nonempty (not non-empty)
  • nonincreasing (not non-increasing)
  • nonnegative (not non-negative)
  • nonpositive (not non-positive)
  • nonprime (not non-prime)
  • nonsquare (not non-square)
  • nonsquarefree (not non-squarefree)
  • nontrivial (not non-trivial)
  • nonunit (not non-unit)
  • nonzero (not non-zero)
  • occurring (not occuring or ocurring)
  • octagon, not 8-gon: prefixes are used for figurate numbers below 9
  • p(n) is sometimes (but not always) the number of partitions of n (A000041)
  • phi for the golden ratio (sometimes tau), phi(n) for the Euler totient function A000010.
  • Pi for 3.141592653... (not pi)
  • prime(n) (not p(n) or Prime(n), etc.) for the n-th prime
  • prime-indexed prime (not prime-index prime)
  • Product_{k=a..b} for product notation (always use capital "P")
  • proved (not proven)
  • recurrence (not recurence or reccurrence)
  • recurring (not recuring or reccurring)
  • semiprime (not semi-prime)
  • sin(x) (not Sin[x])
  • spaces: one space, not two, after the end of a sentence
  • sqrt (not √)
  • squarefree (not square-free)
  • submatrix (not sub-matrix)
  • Sum_{k=a..b} for summation notation (always use capital "S")
  • tetranacci (not Tetranacci)
  • triangular (not Triangular, unless at the beginning of a sentence)
  • tribonacci (not Tribonacci)
  • zeroth (not zeroeth)
  • zeros (not zeroes)

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.

Technical definitions

  • Divisors - often a source of confusion!
    • divisors: number 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"
    • 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? A lot of contributors to the OEIS find this confusing.
    • a == b (mod c) means that a-b is a multiple of 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 b-file, and all the terms - with gaps, question marks, or ranges for the uncertain terms - in an a-file. Example: A072942, which has both a b-file and an a-file. A046057 is a sequence from group theory which has an a-file although we don't know enough terms for certain to give a b-file.
  • 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 the sequence produced by the generating function. Example: A008368, arising from the face-centered 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 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 sequence involving such numbers are conjectural. For example, see A004061, numbers n such that (5^n-1)/4 is prime.
  • See also the entry in the Index to the OEIS for conjectured sequences.

See also

OEIS sequence entry fields
Name · Data · Offset · Comments · References · Links · Formula · Example · Maple · Mathematica · Prog · Crossrefs · Keyword · Author · Extensions
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