Sequences - Xref - Sequences - eval

<?php

  // The walks run far - up to two million candidates - and the gate fetches twelve cases at
  // once: the five seconds a sequence has by default ran out on a busy machine and the
  // answer came back short. The budget is not what this case asserts. Nor is PHP's own limit:
  // on a loaded machine the walk took more than its 30 seconds of processor time and the
  // case ended on "Maximum execution time exceeded".

  $padSeqMaxSeconds = 60;

  set_time_limit ( 120 );

?>

[{sequence eval='100 - @', rows=3}{$sequence} {/sequence}][{sequence '1;50;99', flag, eval='100 - @'}{$sequence}{/sequence}][{sequence '-3;-2;-1', flag, eval='@ * -1'}{$sequence}{/sequence}][{sequence '0;1;2;3', flag, eval='@ % 4'}{$sequence}{/sequence}][{sequence '0.5;1;1.5', flag, eval='@ / 2'}{$sequence}{/sequence}][{sequence '8.5;3.5', flag, step=2.5}{$sequence}{/sequence}][{sequence '3.5;8.5', flag, step=2.5}{$sequence}{/sequence}][{sequence '2.5;7.5;5', flag, floor=2.5}{$sequence}{/sequence}][{sequence '30000;30001', flag, eval='@ * 2'}{$sequence}{/sequence}]

<?php

  // A value spliced into the quoted expression of the eval sequence is a string of it in every
  // spelling - {eval '...'}, {sequence:eval '...'}, make='eval|...', sequence:eval(2, '...') -
  // as in eval='...': only eval= quoted it, and in the others the value became part of the
  // expression and called the function it named.

  $q = 'php:gettype()';

?>

e[{eval '@ . {$q}', rows=2}{$eval} {/eval}] s[{sequence:eval '@ . {$q}', rows=2}{$eval} {/sequence:eval}] m[{sequence '1..2', make='eval|@ . {$q}'}{$sequence} {/sequence}] c[{echo sequence:eval(2, '@ . {$q}')}]

{sequence eval='@ * 2', rows=8}
  {$sequence},
{/sequence}

<?php

  // The parameter of sequence:eval() written as a quoted string is an expression the template
  // writes, and runs - the third term of '@ * 2' is 6. It was refused as one from a value,
  // which sequence:eval(3, $q) still is.

?>

a[{echo sequence:eval(3, '@ * 2')}] b[{echo sequence:eval(4, "@ + 10")}]

<?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}";

?>