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Template:Sequence/list/names

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The {{sequence/list/names}} (or {{seq/list/names}}) database template uses sequence names "database" tables templates (of A-numbers and their respective sequence names) and is intended to be used by the {{sequence}} OEIS Wiki user interface template (which shows a tooltip with the sequence name).

Contents of sequence names database tables

Autopopulating the sequence names database tables via a script

The sequence names "database" is to be split in sections (tables), with 1000 sequence names per table. The sequence names "database" tables would likely have to be autopopulated via a script, since there are currently (as of June 2012) more than 200000 sequences!

A000000..A099999
A000000..A009999
{{seq/list/names/A000000..A000999}}
{{seq/list/names/A001000..A001999}}
{{seq/list/names/A002000..A002999}}
{{seq/list/names/A003000..A003999}}
{{seq/list/names/A004000..A004999}}
{{seq/list/names/A005000..A005999}}
{{seq/list/names/A006000..A006999}}
{{seq/list/names/A007000..A007999}}
{{seq/list/names/A008000..A008999}}
{{seq/list/names/A009000..A009999}}
A010000..A019999
{{seq/list/names/A010000..A010999}}
{{seq/list/names/A011000..A011999}}
{{seq/list/names/A012000..A012999}}
{{seq/list/names/A013000..A013999}}
{{seq/list/names/A014000..A014999}}
{{seq/list/names/A015000..A015999}}
{{seq/list/names/A016000..A016999}}
{{seq/list/names/A017000..A017999}}
{{seq/list/names/A018000..A018999}}
{{seq/list/names/A019000..A019999}}
A020000..A029999
{{seq/list/names/A020000..A020999}}
{{seq/list/names/A021000..A021999}}
{{seq/list/names/A022000..A022999}}
{{seq/list/names/A023000..A023999}}
{{seq/list/names/A024000..A024999}}
{{seq/list/names/A025000..A025999}}
{{seq/list/names/A026000..A026999}}
{{seq/list/names/A027000..A027999}}
{{seq/list/names/A028000..A028999}}
{{seq/list/names/A029000..A029999}}
A030000..A039999
{{seq/list/names/A030000..A030999}}
{{seq/list/names/A031000..A031999}}
{{seq/list/names/A032000..A032999}}
{{seq/list/names/A033000..A033999}}
{{seq/list/names/A034000..A034999}}
{{seq/list/names/A035000..A035999}}
{{seq/list/names/A036000..A036999}}
{{seq/list/names/A037000..A037999}}
{{seq/list/names/A038000..A038999}}
{{seq/list/names/A039000..A039999}}
A040000..A049999
{{seq/list/names/A040000..A040999}}
{{seq/list/names/A041000..A041999}}
{{seq/list/names/A042000..A042999}}
{{seq/list/names/A043000..A043999}}
{{seq/list/names/A044000..A044999}}
{{seq/list/names/A045000..A045999}}
{{seq/list/names/A046000..A046999}}
{{seq/list/names/A047000..A047999}}
{{seq/list/names/A048000..A048999}}
{{seq/list/names/A049000..A049999}}
A050000..A059999
{{seq/list/names/A050000..A050999}}
{{seq/list/names/A051000..A051999}}
{{seq/list/names/A052000..A052999}}
{{seq/list/names/A053000..A053999}}
{{seq/list/names/A054000..A054999}}
{{seq/list/names/A055000..A055999}}
{{seq/list/names/A056000..A056999}}
{{seq/list/names/A057000..A057999}}
{{seq/list/names/A058000..A058999}}
{{seq/list/names/A059000..A059999}}
A060000..A069999
{{seq/list/names/A060000..A060999}}
{{seq/list/names/A061000..A061999}}
{{seq/list/names/A062000..A062999}}
{{seq/list/names/A063000..A063999}}
{{seq/list/names/A064000..A064999}}
{{seq/list/names/A065000..A065999}}
{{seq/list/names/A066000..A066999}}
{{seq/list/names/A067000..A067999}}
{{seq/list/names/A068000..A068999}}
{{seq/list/names/A069000..A069999}}
A070000..A079999
{{seq/list/names/A070000..A070999}}
{{seq/list/names/A071000..A071999}}
{{seq/list/names/A072000..A072999}}
{{seq/list/names/A073000..A073999}}
{{seq/list/names/A074000..A074999}}
{{seq/list/names/A075000..A075999}}
{{seq/list/names/A076000..A076999}}
{{seq/list/names/A077000..A077999}}
{{seq/list/names/A078000..A078999}}
{{seq/list/names/A079000..A079999}}
A080000..A089999
{{seq/list/names/A080000..A080999}}
{{seq/list/names/A081000..A081999}}
{{seq/list/names/A082000..A082999}}
{{seq/list/names/A083000..A083999}}
{{seq/list/names/A084000..A084999}}
{{seq/list/names/A085000..A085999}}
{{seq/list/names/A086000..A086999}}
{{seq/list/names/A087000..A087999}}
{{seq/list/names/A088000..A088999}}
{{seq/list/names/A089000..A089999}}
A090000..A099999
{{seq/list/names/A090000..A090999}}
{{seq/list/names/A091000..A091999}}
{{seq/list/names/A092000..A092999}}
{{seq/list/names/A093000..A093999}}
{{seq/list/names/A094000..A094999}}
{{seq/list/names/A095000..A095999}}
{{seq/list/names/A096000..A096999}}
{{seq/list/names/A097000..A097999}}
{{seq/list/names/A098000..A098999}}
{{seq/list/names/A099000..A099999}}

A100000..A199999
A100000..A109999
{{seq/list/names/A100000..A100999}}
{{seq/list/names/A101000..A101999}}
{{seq/list/names/A102000..A102999}}
{{seq/list/names/A103000..A103999}}
{{seq/list/names/A104000..A104999}}
{{seq/list/names/A105000..A105999}}
{{seq/list/names/A106000..A106999}}
{{seq/list/names/A107000..A107999}}
{{seq/list/names/A108000..A108999}}
{{seq/list/names/A109000..A109999}}
A110000..A119999
{{seq/list/names/A110000..A110999}}
{{seq/list/names/A111000..A111999}}
{{seq/list/names/A112000..A112999}}
{{seq/list/names/A113000..A113999}}
{{seq/list/names/A114000..A114999}}
{{seq/list/names/A115000..A115999}}
{{seq/list/names/A116000..A116999}}
{{seq/list/names/A117000..A117999}}
{{seq/list/names/A118000..A118999}}
{{seq/list/names/A119000..A119999}}
A120000..A129999
{{seq/list/names/A120000..A120999}}
{{seq/list/names/A121000..A121999}}
{{seq/list/names/A122000..A122999}}
{{seq/list/names/A123000..A123999}}
{{seq/list/names/A124000..A124999}}
{{seq/list/names/A125000..A125999}}
{{seq/list/names/A126000..A126999}}
{{seq/list/names/A127000..A127999}}
{{seq/list/names/A128000..A128999}}
{{seq/list/names/A129000..A129999}}
A130000..A139999
{{seq/list/names/A130000..A130999}}
{{seq/list/names/A131000..A131999}}
{{seq/list/names/A132000..A132999}}
{{seq/list/names/A133000..A133999}}
{{seq/list/names/A134000..A134999}}
{{seq/list/names/A135000..A135999}}
{{seq/list/names/A136000..A136999}}
{{seq/list/names/A137000..A137999}}
{{seq/list/names/A138000..A138999}}
{{seq/list/names/A139000..A139999}}
A140000..A149999
{{seq/list/names/A140000..A140999}}
{{seq/list/names/A141000..A141999}}
{{seq/list/names/A142000..A142999}}
{{seq/list/names/A143000..A143999}}
{{seq/list/names/A144000..A144999}}
{{seq/list/names/A145000..A145999}}
{{seq/list/names/A146000..A146999}}
{{seq/list/names/A147000..A147999}}
{{seq/list/names/A148000..A148999}}
{{seq/list/names/A149000..A149999}}
A150000..A159999
{{seq/list/names/A150000..A150999}}
{{seq/list/names/A151000..A151999}}
{{seq/list/names/A152000..A152999}}
{{seq/list/names/A153000..A153999}}
{{seq/list/names/A154000..A154999}}
{{seq/list/names/A155000..A155999}}
{{seq/list/names/A156000..A156999}}
{{seq/list/names/A157000..A157999}}
{{seq/list/names/A158000..A158999}}
{{seq/list/names/A159000..A159999}}
A160000..A169999
{{seq/list/names/A160000..A160999}}
{{seq/list/names/A161000..A161999}}
{{seq/list/names/A162000..A162999}}
{{seq/list/names/A163000..A163999}}
{{seq/list/names/A164000..A164999}}
{{seq/list/names/A165000..A165999}}
{{seq/list/names/A166000..A166999}}
{{seq/list/names/A167000..A167999}}
{{seq/list/names/A168000..A168999}}
{{seq/list/names/A169000..A169999}}
A170000..A179999
{{seq/list/names/A170000..A170999}}
{{seq/list/names/A171000..A171999}}
{{seq/list/names/A172000..A172999}}
{{seq/list/names/A173000..A173999}}
{{seq/list/names/A174000..A174999}}
{{seq/list/names/A175000..A175999}}
{{seq/list/names/A176000..A176999}}
{{seq/list/names/A177000..A177999}}
{{seq/list/names/A178000..A178999}}
{{seq/list/names/A179000..A179999}}
A180000..A189999
{{seq/list/names/A180000..A180999}}
{{seq/list/names/A181000..A181999}}
{{seq/list/names/A182000..A182999}}
{{seq/list/names/A183000..A183999}}
{{seq/list/names/A184000..A184999}}
{{seq/list/names/A185000..A185999}}
{{seq/list/names/A186000..A186999}}
{{seq/list/names/A187000..A187999}}
{{seq/list/names/A188000..A188999}}
{{seq/list/names/A189000..A189999}}
A190000..A199999
{{seq/list/names/A190000..A190999}}
{{seq/list/names/A191000..A191999}}
{{seq/list/names/A192000..A192999}}
{{seq/list/names/A193000..A193999}}
{{seq/list/names/A194000..A194999}}
{{seq/list/names/A195000..A195999}}
{{seq/list/names/A196000..A196999}}
{{seq/list/names/A197000..A197999}}
{{seq/list/names/A198000..A198999}}
{{seq/list/names/A199000..A199999}}

Format of sequence names database tables

The sequence names "database" tables format is the following:

  • each line of the database table must have the format (including one space before the vertical pipe)
| A-number = Sequence name (text only, or HTML character entities; NO HTML tags).
  • the following characters cannot be used
    • | (vertical pipe) (using {{!}} instead doesn't fix the problem...) (look at A000099 example below, the name got truncated!)
    • " (double quote) (use " HTML character entity instead)
  • HTML and TeX tags cannot be used
    • log<sub>10</sub> (show as log_10 instead)
    • <math>log_{10}</math> (show as log_10 instead)
    • e<sup>x</sup> (show as e^x instead)
    • <math>e^x</math> (show as e^x instead)
  • wikitext cannot be used
    • [[...]] (messes up the sequence name tooltip created with {{sequence}} via the {{tooltip}} template)

Usage

{{sequence/list/names|A-number = A-number}}

or

{{sequence/list/names|A-number}}

or

{{seq/list/names|A-number = A-number}}

or

{{seq/list/names|A-number}}

Examples

Examples with valid input

Code Result
{{seq/list/names|A0}} The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!)
{{seq/list/names|A1}} Number of groups of order n.
{{seq/list/names|A01}} Number of groups of order n.
{{seq/list/names|A2}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's.
{{seq/list/names|A002}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's.
{{seq/list/names|A3}} Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n.
{{seq/list/names|A37}} Numbers that are not squares.
{{seq/list/names|A037}} Numbers that are not squares.

Code Result Comment
{{seq/list/names|A000000}} The empty sequence. (Although not in the Main OEIS, since it is NOT searchable!)
{{seq/list/names|A000001}} Number of groups of order n.
{{seq/list/names|A000002}} Kolakoski sequence: a(n) is length of n-th run; a(1) = 1; sequence consists just of 1's and 2's.
{{seq/list/names|A000003}} Number of classes of primitive binary forms of discriminant D = -4n; or equivalently class number of quadratic order of discriminant D = -4n.
{{seq/list/names|A000004}} The zero sequence.
{{seq/list/names|A000095}} Number of fixed points of GAMMA_0 (n) of type i.
{{seq/list/names|A000096}} n*(n+3)/2.
{{seq/list/names|A000097}} Number of partitions of n if there are two kinds of 1's and two kinds of 2's.
{{seq/list/names|A000098}} Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3.
{{seq/list/names|A000099}} Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); sequence gives values of n where |P(n)| sets a new record. (Name truncated: vertical pipe character not allowed!)

Code Result
{{seq/list/names|A000100}} a(n) = number of compositions of n in which the maximum part size is 3.
{{seq/list/names|A000101}} Increasing gaps between primes (upper end) (compare A002386, which gives lower ends of these gaps).
{{seq/list/names|A000102}} a(n) = number of compositions of n in which the maximum part size is 4.
{{seq/list/names|A000103}} Number of n-node triangulations of sphere in which every node has degree >= 4.
{{seq/list/names|A000104}} Number of n-celled polyominoes without holes.
{{seq/list/names|A000195}} log(n) rounded down.
{{seq/list/names|A000196}} Integer part of square root of n. Or, number of squares <= n. Or, n appears 2n+1 times.
{{seq/list/names|A000197}} (n!)!.
{{seq/list/names|A000198}} Largest order of automorphism group of a tournament with n nodes.
{{seq/list/names|A000199}} Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).

Code Result
{{seq/list/names|A000200}} Number of bicentered hydrocarbons with n atoms.
{{seq/list/names|A000201}} Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2.
{{seq/list/names|A000202}} a(8i+j) = 13i + a(j), where 1<=j<=8.
{{seq/list/names|A000203}} sigma(n) = sum of divisors of n. Also called sigma_1(n).
{{seq/list/names|A000204}} Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.
{{seq/list/names|A000295}} Eulerian numbers (Euler's triangle: column k=2 of A008292, column k=1 of A173018)
{{seq/list/names|A000296}} Number of partitions of an n-set into blocks of size >1. Also number of cyclically spaced (or feasible) partitions.
{{seq/list/names|A000297}} (n+1)*(n+3)*(n+8)/6.
{{seq/list/names|A000298}} Number of partitions into non-integral powers.
{{seq/list/names|A000299}} Number of n-node rooted trees of height 4.

Code Result
{{seq/list/names|A000400}} Powers of 6.
{{seq/list/names|A000401}} Numbers of form x^2 + y^2 + 2z^2.
{{seq/list/names|A000402}} Number of permutations of [n] in which the longest increasing run has length 3.
{{seq/list/names|A000403}} Number of simple equifacetted 3-manifolds with n faces.
{{seq/list/names|A000404}} Numbers that are the sum of 2 nonzero squares.
{{seq/list/names|A000495}} Nearest integer to sinh(n).
{{seq/list/names|A000496}} Restricted permutations.
{{seq/list/names|A000497}} S2(j,2j+2) where S2(n,k) is a 2-associated Stirling number of the second kind.
{{seq/list/names|A000498}} Eulerian numbers (Euler's triangle: column k=4 of A008292, column k=3 of A173018)
{{seq/list/names|A000499}} Related to the divisor function.

Code Result
{{seq/list/names|A000900}} Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).
{{seq/list/names|A000901}} Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details).
{{seq/list/names|A000902}} E.g.f.: (1/2)*(exp(2x + x^2) + 1).
{{seq/list/names|A000903}} Number of inequivalent ways of placing n nonattacking rooks on n X n board.
{{seq/list/names|A000904}} a(n) = (n + 1) a(n - 1) + (n + 2) a(n - 2) + a(n - 3); a(1)=0, a(2)=3, a(3)=13.
{{seq/list/names|A000995}} Shifts left two terms under the binomial transform.
{{seq/list/names|A000996}} Shifts 3 places left under binomial transform.
{{seq/list/names|A000997}} From a differential equation.
{{seq/list/names|A000998}} From a differential equation.
{{seq/list/names|A000999}} 5^a(n) divides C(2n,n).

Code Result
{{seq/list/names|A100000}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100001}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100002}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100003}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100004}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100095}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100096}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100097}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100098}} Template:Sequence/list/names/A100000..A100999
{{seq/list/names|A100099}} Template:Sequence/list/names/A100000..A100999

Examples with invalid input

Code Result
{{seq/list/names}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|45}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|a-100}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|a100000}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|B100000}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|A1000000}} Sequence/list error: Argument must be an A-number between A000000 and A999999!
{{seq/list/names|A}} Sequence/list error: Argument must be an A-number!
{{seq/list/names|A100012!}} Sequence/list error: Argument must be an A-number!

Code

<noinclude>{{Documentation}}</noinclude><includeonly><!--

-->{{#ifeq: {{#pos:{{{A-number|{{{1|}}}}}}|A}} | 0
| {{ifinteger| {{#if: {{#sub:{{{A-number|{{{1|}}}}}}|1}} | {{#sub:{{{A-number|{{{1|}}}}}}|1}} | NOTINT! }} 
  | {{#ifexpr: ( ( {{#sub:{{{A-number|{{{1|}}}}}}|1}} ) >= 0 ) and ( ( {{#sub:{{{A-number|{{{1|}}}}}}|1}} ) <= 999999 )  
    | {{#switch: {{#expr: floor ( ( {{#sub:{{{A-number|{{{1|}}}}}}|1}} ) / 1000 ) }}

      |    0 = {{sequence/list/names/A000000..A000999| {{{A-number|{{{1|}}}}}} }}
      |    1 = {{sequence/list/names/A001000..A001999| {{{A-number|{{{1|}}}}}} }} 
      |    2 = {{sequence/list/names/A002000..A002999| {{{A-number|{{{1|}}}}}} }} 
      |    3 = {{sequence/list/names/A003000..A003999| {{{A-number|{{{1|}}}}}} }} 
      |    4 = {{sequence/list/names/A004000..A004999| {{{A-number|{{{1|}}}}}} }} 
      |    5 = {{sequence/list/names/A005000..A005999| {{{A-number|{{{1|}}}}}} }} 
      |    6 = {{sequence/list/names/A006000..A006999| {{{A-number|{{{1|}}}}}} }} 
      |    7 = {{sequence/list/names/A007000..A007999| {{{A-number|{{{1|}}}}}} }} 
      |    8 = {{sequence/list/names/A008000..A008999| {{{A-number|{{{1|}}}}}} }} 
      |    9 = {{sequence/list/names/A009000..A009999| {{{A-number|{{{1|}}}}}} }}
 
      (...)

      |  190 = {{sequence/list/names/A190000..A190999| {{{A-number|{{{1|}}}}}} }}
      |  191 = {{sequence/list/names/A191000..A191999| {{{A-number|{{{1|}}}}}} }} 
      |  192 = {{sequence/list/names/A192000..A192999| {{{A-number|{{{1|}}}}}} }} 
      |  193 = {{sequence/list/names/A193000..A193999| {{{A-number|{{{1|}}}}}} }} 
      |  194 = {{sequence/list/names/A194000..A194999| {{{A-number|{{{1|}}}}}} }} 
      |  195 = {{sequence/list/names/A195000..A195999| {{{A-number|{{{1|}}}}}} }} 
      |  196 = {{sequence/list/names/A196000..A196999| {{{A-number|{{{1|}}}}}} }} 
      |  197 = {{sequence/list/names/A197000..A197999| {{{A-number|{{{1|}}}}}} }} 
      |  198 = {{sequence/list/names/A198000..A198999| {{{A-number|{{{1|}}}}}} }} 
      |  199 = {{sequence/list/names/A199000..A199999| {{{A-number|{{{1|}}}}}} }}
 
      | {{{A-number|{{{1|}}}}}} <!-- NOT in sequence names database table (return the A-number) -->
      }}
    | {{error| Sequence/list error: Argument must be an [[A-number]] between A000000 and A999999! }} 
    }}
  | {{error| Sequence/list error: Argument must be an [[A-number]]! }}
  }}
| {{error| Sequence/list error: Argument must be an [[A-number]]! }} 
}}<!--

--></includeonly><noinclude>
[[Category:Integer sequences|*]]
[[Category:Mathematics-related lists|Sequences]]
[[Category:Mathematical tables|Sequences]]
[[Category:Database table templates|Sequences]]
</noinclude>