Sequences - Xref - Sequences - repeat

<?php

  // Only a literal parameter of the eval sequence is an expression the template wrote: the
  // value spliced into sequence:repeat(2, '...') was taken for one, and sequence:eval(2, $q),
  // refused on its own, then ran the same value from the request.

  $q = '0 + php:abs(-3)';

?>

{echo sequence:repeat(2, '{$q}')}{echo sequence:eval(2, $q)}

[{prime 5}{$prime} {/prime}][{fibonacci 5}{$fibonacci} {/fibonacci}][{keep:prime '1..10'}{$sequence} {/keep:prime}][{flag:even '1;2;3'}{$sequence}{/flag:even}][{multiply 3, rows=3}{$multiply} {/multiply}][{repeat 'x', rows=2}{$repeat}{/repeat}]

<?php

  $up   = '1...1e400';
  $down = '-1e400...-5';

?>

[{sequence 'repeat', $up, rows=20}{if $sequence lt 1}low {/if}{/sequence}][{sequence 'repeat', $down, rows=20}{if $sequence gt -5}high {/if}{/sequence}][{sequence '1;1;1;1;1;1', make, add=$up}{if $sequence lt 2}low {/if}{/sequence}]

[{sequence 'prime'}{$sequence} {/sequence}][{set $t = 'fibonacci'}{sequence $t, rows=5}{$sequence} {/sequence}]{sequence '1..5', push='s'}{/sequence}[{sequence 's'}{$sequence} {/sequence}][{action 's', reverse}{$sequence} {/action}][{keep 'odd', s}{$sequence} {/keep}][{pull:s 'reverse'}{$sequence} {/pull:s}][{repeat 'prime', rows=2}{$repeat} {/repeat}][{sequence 'sum', from=1, to=4}{$sequence}{/sequence}]

{sequence repeat=3, rows=8}
  {$sequence},
{/sequence}

[{echo sequence:repeat(2)}][{echo sequence:repeat(2, 1)}][{echo sequence:repeat(5, 1)}][{echo sequence:repeat(5)}][{sequence '1..5', keep, range}{$sequence} {/sequence}][{sequence '1..5', keep, range=1}{$sequence} {/sequence}][{sequence '1..5', keep, repeat}{$sequence} {/sequence}][{sequence '1..5', keep, repeat=1}{$sequence} {/sequence}][{sequence '1..5', keep, range}{$sequence} {/sequence}]

{sequence repeat=5, rows=4, unique}
  {$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

  // Listen: a sequence played as notes. Each of the first 32 terms becomes a note - the
  // term modulo 60, five octaves up from C2, the way the OEIS 'listen' button folds a term
  // into the keyboard - and the notes are written as a WAV file into the page itself
  // (seqFunWav in _lib/fun.php), so an <audio> element plays them without JavaScript.
  // Recamán's sequence, which jumps back and forth, is the famous one to listen to.
  //
  // type arrives from the query string and is used only when it names a type the gallery
  // draws.

  $choices = seqFunTypes ();

  if ( ! isset ( $type ) or ! is_string ( $type ) or ! in_array ( $type, $choices ) )
    $type = 'recaman';

  $terms = seqFunTerms ( $type, 32 );
  $oeis  = seqFunOeis ( $terms, $type );
  $oeis  = $oeis ? sprintf ( 'A%06d', $oeis ) : '';
  $list  = implode ( ', ', $terms );
  $notes = implode ( ' ', array_map ( 'seqFunNoteName', seqFunNotes ( $terms ) ) );
  $audio = seqFunWav ( $terms );

?>

<p>{choices}{notFirst} | {/notFirst}{if $choices eq $type}<b>{$choices}</b>@else@<a href="?listen&type={$choices}">{$choices}</a>{/if}{/choices}</p>

<h3>{$type | ucfirst}{if $oeis ne ''} - <a href="https://oeis.org/{$oeis}">{$oeis}</a>{/if}</h3>

{chart 'line', data='terms', title='{$type | ucfirst}, the first 32 terms', width=640, height=220}

<p><audio controls preload="none" src="{$audio}"></audio></p>

<p>Each term is a note: the term modulo 60, counted in semitones up from C2.</p>

<p><small>{$list}</small></p>

<p><small>{$notes}</small></p>

<?php

  echo "{table}";

  echo str_pad ( "{demo}{sequence}", 38) . "{\$sequence} {/sequence} {/demo}";

  foreach ( types () as $type ) {

    $parm = pqParm ( $type );

        if ( $type == 'oeis'      ) $gox = "oeis=87";
    elseif ( $type == 'list'      ) $gox = "list='1;8;5;2;9;66'";
    elseif ( $type == 'range'     ) $gox = "range='1..10'";
    elseif ( $type == 'eval'      ) $gox = "eval='@ * 10 | @ - 1'";
    elseif ( $type == 'random'    ) $gox = 'random, maximal=99';
    else                            $gox = "$type$parm";

    echo str_pad ( "{demo}{sequence $gox}", 38) . "{\$sequence} {/sequence} {/demo}";

  }

  echo "{/table}";

?>