Overview of the contribution process
Make sure your sequence is not already in the OEIS. Look up the sequence, omitting the first couple of terms. Look up terms 2 through 12, say. Check your calculations! After more than 50 years, most of the obvious sequences are already in the OEIS.
If you don't have a specific sequence in mind, but just a general idea for new sequences, work out the simplest cases, and see if they are already in the OEIS (see above). If they are not in the OEIS, the next step could be to send a message to the Sequence Fans Mailing List asking for help in computing your sequences.
Before submitting your new sequence, search the OEIS for related sequences to mention as cross-references, and check the Internet for relevant books and articles. If you wants to add a sequence to the OEIS and you have verified it's not already in the OEIS, then perhaps is already in the OEIS, and should be mentioned as a cross-reference.
The next step is to log on to the OEIS, and click "Contribute New Sequence or Comment". Once you start filling out the form to contribute a new sequence, the system finds the next available A-number, changes the name to something like "allocated for David Smith," puts keyword:allocated in the Keywords field and sets status to approved.
The proposal stage
With the A-number allocated and faced with the blank entry form, there are two ways to go about the next step: either fill in the bare minimum (a title, a few terms, and the offset) and click "Save changes," or try to fill in as much as you can before saving. Once you click "save", the status is changed to editing.
There is now time to polish the entry, so take your time. Just don't let more than a week go by without any activity. All the relevant fields should be filled in, except the Extensions field (that may be used in the next stage of the process). For example, you could add a Maple program in the Maple field. Although the system automatically fills in some of the keywords for the Keywords field, you might have to make changes to it; see clear-cut examples of keywords if you're not sure what should be done in that field.
We don't expect you to know everything there is to know about a sequence. But we do expect you to make an effort to answer the basic questions, such as How is the sequence defined? What are examples to illustrate the first few terms? Why is the sequence interesting? Is the sequence finite? Does the sequence contain negative terms? It's OK to say things like "I believe the sequence is finite" or "I have checked up to 10 12 and found no more terms."
Always distinguish between a guess and a theorem. If you say that there are infinitely many terms, you should have a proof. Otherwise you must say "It appears that there are infinitely many terms".
Once you're ready to have the editors look at your sequence, click the button "These changes are ready for review by an OEIS Editor." This changes the status from editing to proposed. (Don't worry if you click that prematurely, you can always save another change to bring the status back to editing.)
The suggested pre-submit checklist has advice on what to do before moving to the next stage.
The review stage
Depending on backlog, it may be anywhere from a few minutes to a couple of months after the sequence is proposed before an OEIS Editor looks at it. The Editors will first try to understand the definition, and then they will try to make sure that all the logic and arithmetic in the entry is correct, and that the entry conforms to the OEIS Style Sheet. In general, the more diligent you are in the proposal stage, the smoother and faster the review stage goes. You might read the page Why are my submissions taking so long to be accepted.
"Pink box comments" are an important tool at this stage. At the bottom of the draft, there is a text box where Editors may ask questions. These appear on the draft in pink boxes. You can use the same text box to answer those questions.
Pink box comments do not become part of the published sequence, but they are part of the permanent record of the sequence, and anyone can see them. For this and other reasons, use discretion.
In some cases, responding will also involve making changes to the sequence, or explaining why a change is not necessary. For example:
|Fri Jan 01||12:08||John Lopez: In the first and second formulas, I think you meant greater than OR equal rather than just greater than.|
|14:22||Michael Smith: You're right about the first formula, I will change it accordingly. But for the second formula, x and y need to be distinct so there's no division by zero in the third formula.|
Editors may also send a sequence back to editing status without making any changes, to indicate that the sequence is not yet ready for publication.
The editors may make more straightforward changes without notice, such as correcting punctuation, grammar, spelling errors, etc. They may also add things that fall within their own area of expertise. An editor familiar with Mathematica may add a Mathematica program, for example.
Depending on the nature of the things the editors change, they may or may not take credit. This is where the Extensions field may come in: suppose an editor adds the next term of a sequence and it's very large and it took a clever algorithm and lot of computer time to get it; there isn't room for people's names in the Data field, so the editor will write something like "a(12) added by John Lopez, Dec 21 2012" in the Extensions field.
At this stage you can also add things to the entry, whether or not the addition is motivated by something an editor says. Such changes don't rate a remark under the Extensions field because they still fall under the umbrella of your "original" authorship (by "original" we mean chronologically to the OEIS). Later additions will be mentioned in that field as needed.
As you and the editors make changes to the draft, the status changes back to editing. Don't change the status back to proposed until the editors' questions are satisfactorily answered. The editors may make changes in increments: touch up some small details, then add a generating function, later add a Maple program, etc. An editor will then change the status back to proposed.
Once the editor is satisfied that the sequence entry is ready to be published, they will click the button "I have reviewed these changes. Mark them ready for approval." Either an Associate Editor or an Editor-in-Chief may do this.
The approval stage
An Editor-in-Chief gives the entry one final once-over. If the sequence is appropriate and ready for publication, they approve the sequence and it appears immediately. If not, they can return the sequence for more editing, usually with a pink-box comment.
The live stage
Once approved, the new sequence entry will come up in the appropriate search results. Anyone with an OEIS account may suggest changes to the entry. These changes go through a miniature version of the process described above (but usually faster unless the changes are major).
It is important to remember that adding a sequence entry to the OEIS is different from writing a poem or a novel. Exhibiting a unique literary voice is not the point at all. Advancements will be made in science and mathematics that may require changes to the sequence entry. And if the sequence does get changed, that is a good thing: it means people are genuinely interested in the concept, interested enough to scrutinize the entry and add things to it.