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标志


提示
(Greetings fromThe On-Line Encyclopedia of Integer Sequences!)
  • The main uses for the OEIS are:
    • to identify a sequence
    • to obtain more terms, formulas, references, links, programs, etc. for a sequence

    You are trying to solve a problem, but it's too hard.
    The answers in the first few cases are1,1,2,4,9,21,51,127
    You then look this upin the OEIS and see if anyone has ever encountered this sequence before (they have).

    Give up?

  • 提示:
    • 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.

      For the example above, you should enter 2,4,9,21,51,127 and leave off the two 1's.

    • Clean up your sequence first.
      • If every other term is zero (e.g. 1 0 2 0 4 0 8 0 16 0 32 0 64 0 ...), omit these zeros, and look up 1 2 4 8 16 32 64 instead.
      • If your sequence has an obvious common factor (e.g. 2 6 12 20 30 42 ...) try dividing it out and look up 1 3 6 10 15 21 instead.

  • Advanced search syntax
    • Examples of searches.
      1,4,9,16,25,36,64
              5 8 13 233 39088169
              "fermat's little theorem"
              author:Guy keyword:nice
              keyword:nice keyword:more -keyword:base
              keyword:new -keyword:base
              id:A64413
              A64413
              id:A028284|id:A066948
              author:njas keyword:less|keyword:dumb
      • The search text is a list of space-separated search terms, as with popular web search engines.
      • The search terms can be single numbers, sequences of numbers, words or strings of words.
      • Sequences of numbers should be separated with commas.
      • Strings of words should be separated by spaces (NOT commas).
      • Strings of words may be enclosed in double quotes.
      • You can separate search terms with | (no spaces around the |) and it means sequences that match either term.

    • Commas versus spaces.Commas and spaces have different meanings. These two searches produce different results:
      1,4,9,16,25,36,49,64,81,100
              1 4 9 16 25 36 49 64 81 100
      The first matches sequences in which the numbers appear consecutively, in the order given.
      The second matches sequences containing all the numbers, in any order.
      Both searches will match the squares (A000290), but the second will also match other sequences,
      such as the composite numbers (A002808), which contain all those numbers but not necessarily consecutively or in the given order.

      The same is true for word searches. Suppose you want to find sequences that cite Stanley's book Enumerative Combinatorics.
      The search string Stanley, Combinatorics (with the comma) gets no hits, but searching for Stanley Combinatorics (without the comma) gets several hundred hits.

    • Prefixes.
      Simple search terms will be matched against every field of the entry,
      though fields such as the name and the sequence data are given more weight than others.
      Prefixes restrict the search to particular lines, as in:
      keyword:nice author:LeBrun
      The prefixes mostly correspond to the lines in the display, as follows:
      id:                     ref:                    program:
              seq:                    link:                   xref:
              signed:                 formula:                keyword:
              name:                   example:                author:
              offset:                 maple:                  extension:
              comment:                mathematica:
      • id:A001006displays sequence A001006.A001006displays sequence A001006 followed by all other sequences that mention it.
      • seq:matches the sequence data, possibly by ignoring signs.
      • 签署:matches sequence data and requires that any signs match as well. 例如
        signed:1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0
        will find the Moebius function mu(n), A008683.
      • Put a minus sign in front of a prefix to exclude those matches.
        Put a tilde (~) in front of a number to exclude it (only applies if the numbers are separated by spaces).
        For example, a search for 2 4 ~8 16 returns sequences such as 0, 1, 2, 4, 16, 65536 that do not contain 8.
      • You can say prefix: by itself to match sequences that have a line of that type.
        例如裁判:will match all sequences with reference lines.
      • Another example: you can say, e.g. -seq:5 in your search to exclude all sequences containing the number 5. So if you know your sequence consists only of 1, 2, 3, and 4 (and does include all of them), you could search seq:1 seq:2 seq:3 seq:4 -seq:5 -seq:6 -seq:0.

      Two other prefixes are concerned with subsequences:

      subseq:                 signedsubseq:
      • You can say, for example, subseq:377,8 to get those numbers in sequence data in that order.
    • 相关性
      The results are returned in order of “relevance,” which is a rough measure of how likely you are to want to see a particular sequence.
      It orders first by how well the sequence matched the search terms,
      second by the popularity of the sequence in other sequences' cross-references,
      and finally by sequence number.
      Other sort orders can be selected on the results page.

    • Wild cards.
      • The wildcard _ will match any number in a sequence, as in 1,2,_,4,5
      • The wildcard __ will match any list of numbers in a sequence, as in 1,2,__,7,8
      • Search terms are highlighted in the results
    • Punctuationis not indexed and is treated as identical to whitespace during matching;
      for example, searching forfermat'sis the same as searching for"fermat s"

    • Further examples
      • To find sequences containing both terms 1759 and 1957: search for"seq:1759 seq:1957"

  • Further Hints
    • You can only look up a sequence of integers or whole numbers, like 6 or 10 or -3
      • If you have a sequence of fractions,look up numerators and denominators separately
        Example: for

        1/4, 5/8, 13/16, 29/32, 61/64, 125/128, ...,

        look up 1,5,13,29,61,125 and 4,8,16,32,64,128 separately.
      • If your sequence hasdecimal fractionsin it (1.4, 5.87, 12.083), the OEIS probably can't help you
        (though you might try rounding them to the nearest integer, or taking the integer part).
      • There are no letter sequences (such as A, B, C, D ...) in the OEIS!

    • For a triangle of numbers,such as:
      1                        
               1   1                      
             1   2   2                    
           1   3   5   4                  
         1   4   9  12   9                
       1   5  14  25  30  21
      etc., make it into a sequence by reading across the rows:

      1 2 2 1 3 5 4 1 4 9

      and look that up. Or look up the diagonals, such as

      1 2 5 12 30 76

    • For a square array,such as
      1   1   1   1 ...
          1   2   3   4 ...
          2   5   9  14 ...
          4  12  25  44 ...
          9  30  69 133 ...
         21  76 189 392 ...
      etc., make it into a sequence by reading up (or down) theantidiagonals

      1 1 1 1 2 2 1 3 5 4 1 4 9

      and look that up. Or look up the rows or columns, such as

      1 2 5 12 30 76

    • For a decimal constant,such as 3.14159, look up the sequence of digits, as in

      3 1 4 1 5 9

      The OEIS search engine will convert numbers containing decimal points into digit sequences automatically,
      so you can type 3.14159 directly.
    • To searchfor a single large numberin the OEIS, try Google, because Google has searched all the .txt files in the OEIS, and so may do a better job than the OEIS search engine. Example: The 64th Motzkin number is 9468017265749942384739441267, and Google will tell you it is in theb-fileA001006
  • 这个standard replyreturns nicely reformatted sequences.

    To see the sequences in theinternal formatused in the OEIS, click on the "internal format" link on the results page.
    This is useful when reporting updates or corrections.

  • Note that there is also an<STRONG>Index to the OEIS</strong>
    Hint: To search the指数, ask your favorite search engine, e.g. Google, to search for (say) theta series Index OEIS.

  • 日期have been standardized in the format Jan 01 2001. The month is one of
    Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
    The day is one of 01 02 03 ... 31, and there may be a comma after the day:
    Jan 01 2001 and Jan 01, 2001 are both acceptable.

    So to find the sequences submitted or updated on a particular day, look up both "Oct 10 2001" and "Oct 10, 2000" using the "word" search.

  • Every sequence in the OEIS has anA-number, such asA001850
    If you know the A-number you can retrieve the sequence directly by typing it (with the A) into the search page.

  • If no match is found for your sequence, trySuperseeker

  • If your sequence isn't in the database- and is of general interest - pleasesend it to the OEIS
    This will help other people who come across the same sequence (and will preserve your name for posterity).

  • For a description of a typical entry in the OEIS,点击在这里

  • To browse the OEIS,use theWebCam. This can be set to browse
    • the best sequences
    • recent additions
    • sequences needing more terms, or
    • all sequences.
    For the WebCam to work, Javascript must be turned on. It may not work with some older browsers.

  • The meaning of the little numbers at the right of the blue bar. For example, +30 and 1086 for A000045.
  • For more information, see:

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<font size=-1>Last modified April 23 12:40 EDT 2019. Contains 322386 sequences. (Running on oeis4.)</font>