Sequences - Xref - Sequences - even

[{sequence polite, from=9223372036854775800, rows=2}{$sequence} @else@none{/sequence}][{sequence lucky, from=9223372036854775800, rows=2}{$sequence} @else@none{/sequence}][{sequence even, from=9223372036854775800, rows=2}{$sequence} @else@none{/sequence}][{sequence odd, from=-9223372036854775800, rows=2}{$sequence} @else@none{/sequence}][{sequence polite, from=1000, rows=2}{$sequence} {/sequence}][{sequence lucky, from=1000, rows=2}{$sequence} {/sequence}]

[{sequence even, maximal=10, stop=20}{$sequence} {/sequence}]

[{sequence even, build='check', to=10}{$sequence} {/sequence}][{sequence even, build='bool', to=10}{$sequence} {/sequence}][{sequence odd, build='bool', from=4, to=9}{$sequence} {/sequence}]

[{sequence modulo=7, from=-10000000000000000000, rows=3}{$sequence} {/sequence}][{sequence even, sole=-9223372036854775808}{$sequence} @else@none{/sequence}][{sequence identity, from=9223372036854775806, rows=5}{$sequence} {/sequence}]

[{sequence step=3, build='function', from=2, to=4}{$sequence} {/sequence}][{sequence '2;3;4', make, step=3, build='function'}{$sequence} {/sequence}][{sequence '2;3;4', make, even, build='function'}{$sequence} {/sequence}][{sequence even, build='function', from=2, to=4}{$sequence} {/sequence}][{sequence '1..6', make, odd, build='function'}{$sequence} {/sequence}][{sequence odd, build='function', from=2, to=4}{$sequence} {/sequence}][{sequence step=3, rows=4}{$sequence} {/sequence}][{sequence '2;3;4', make, step=3}{$sequence} {/sequence}][{sequence multiple=3, build='function', from=2, rows=3}{$sequence} {/sequence}][{sequence '1..3', make, multiple=3, build='function'}{$sequence} {/sequence}][{sequence step=3, build='function', increment=2, rows=3}{$sequence} {/sequence}][{sequence even, build='function', rows=3}{$sequence} {/sequence}]

[{sequence even, build='function', from=3000000, rows=3}{$sequence} @else@none{/sequence}][{sequence odd, build='function', from=1000000, rows=3}{$sequence} @else@none{/sequence}][{sequence step=3, build='function', from=1000000, rows=3}{$sequence} @else@none{/sequence}][{sequence multiple=3, build='function', from=1000000, rows=3}{$sequence} @else@none{/sequence}][{sequence '999999;1000000;1000001', make, even, build='function'}{$sequence} @else@none{/sequence}][{sequence even, build='function', from=4611686018427387902, rows=3}{$sequence} @else@none{/sequence}][{sequence step=2.5, build='function', from=3, rows=3}{$sequence} @else@none{/sequence}]

{sequence even, rows=8}
  {$sequence},
{/sequence}

<?php

  $f = '1e400';
  $g = '-1e400';

?>

[{sequence even, from=$f, rows=3}{$sequence} {/sequence}][{sequence odd, from=$f, rows=3}{$sequence} {/sequence}][{sequence even, sole=$g}{$sequence} {/sequence}][{sequence odd, from=$g, rows=3}{$sequence} {/sequence}]

[{sequence even, increment=3, rows=4}{$sequence} {/sequence}][{sequence odd, increment=3, rows=4}{$sequence} {/sequence}][{sequence even, from=2, to=8, increment=2}{$sequence} {/sequence}][{sequence even, rows=3}{$sequence} {/sequence}][{sequence '1..10', increment=2, keep, even}{$sequence} {/sequence}]

[{sequence loop, sole=0}{$sequence} {/sequence}][{flag:even sole=0}{$sequence}{/flag:even}][{flag:even sole=4}{$sequence}{/flag:even}][{set $n = 0}{sequence identity, sole=$n}{$sequence} {/sequence}][{sequence prime, sole=7}{$sequence}{/sequence}][{sequence prime, sole=''}{$sequence} {/sequence}]

{sequence even, from=0, rows=4}
  {$sequence},
{/sequence}

<?php

  // The gallery: every sequence type that needs no parameter, its first 24 terms drawn as a
  // {sparkline}, the first eight written out, and the OEIS entry the terms come from - a
  // link to oeis.org, found in the table the oeis type reads (seqFunOeis in _lib/fun.php).

  $drawn = [];

  foreach ( seqFunTypes () as $type ) {

    $terms = seqFunTerms ( $type, 24 );
    $oeis  = seqFunOeis ( $terms, $type );

    $drawn [] = [
      'type'  => $type,
      'first' => implode ( ', ', array_slice ( $terms, 0, 8 ) ),
      'oeis'  => $oeis ? sprintf ( 'A%06d', $oeis ) : ''
    ];

  }

?>

<p>Every sequence type that needs no parameter, its first 24 terms drawn by
<code>{sparkline sequence=$type, rows=24}</code>, beside the
<a href="https://oeis.org">OEIS</a> entry the terms come from. Follow a name to hear it.</p>

<table cellpadding="4">
  {drawn}
    <tr>
      <td align="right"><a href="?listen&type={$type}">{$type}</a></td>
      <td>{sparkline sequence=$type, rows=24}</td>
      <td align="left"><small>{$first}, ...</small></td>
      <td>{if $oeis ne ''}<a href="https://oeis.org/{$oeis}">{$oeis}</a>{/if}</td>
    </tr>
  {/drawn}
</table>

<?php

  // Front page: names the five ideas the subsystem is built from, and describes the one the
  // concept= parameter asks for.
  //
  // concept arrives from the query string, so it is only used when it names one of them -
  // reading $concepts with an unknown key ended the request with a 500 instead of a page,
  // and so did concept[]=, which arrives as an array.

  $concepts ['sequences']  = 'Something that defines a Sequence list';
  $concepts ['stores']     = 'A stored sequence list';
  $concepts ['actions']    = 'An action executed on a Sequence list';
  $concepts ['plays']      = 'Execute a Sequence on a Sequence';
  $concepts ['resume']     = 'Resume on a stored Sequence';

  if ( ! isset ( $concept ) or ! is_string ( $concept ) or ! isset ( $concepts [$concept] ) )
    $concept = 'sequences';

  $title = 'Sequences';

  $conceptTitle = ucfirst ($concept ) . ' - ' . $concepts [$concept];

?>

{lines}
  {concepts}
    {if &concepts:key NE $concept}
      <a href="?index&go=index&concept={&concepts:key}">{&concepts:key | ucfirst}</a>
    @else@
      <b> {&concepts:key | ucfirst} </b>
    {/if}
    {notLast} | {/notLast}
  {/concepts}
{/lines}

<h2>{$conceptTitle}</h2>

{block}
  {page 'concepts/{$concept}', include}
{/block}