Sequences - Xref - Sequences - ceil

[{sequence modulo='0.0', rows=3}{$sequence} {/sequence}][{sequence modulo='-0', rows=3}{$sequence} {/sequence}][{sequence modulo='00', rows=3}{$sequence} {/sequence}][{sequence '1..3', make, modulo='0.0'}{$sequence} {/sequence}][{sequence ceil='0.0', rows=3}{$sequence} {/sequence}][{sequence floor='-0', rows=3}{$sequence} {/sequence}][{sequence round='00', rows=3}{$sequence} {/sequence}][{sequence '1..3', make, ceil='-0'}{$sequence} {/sequence}][{sequence '1..3', make, floor='0.0'}{$sequence} {/sequence}][{sequence '1..3', make, round='0.0'}{$sequence} {/sequence}][{sequence '1;2;3', flag, floor='-0'}{$sequence}{/sequence}][{sequence '0;1;2', flag, modulo='0.0'}{$sequence}{/sequence}]

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

[{sequence floor=3, from=1000000000000000, rows=3}{$sequence} {/sequence}][{sequence ceil=2, from=100000000000001, rows=2}{$sequence} {/sequence}][{sequence round=5, from=123456789012347, rows=2}{$sequence} {/sequence}][{sequence '1000000000000001;77', make, ceil=2}{$sequence} {/sequence}][{sequence floor=3, from=1000000000000000, rows=3, sum}{$sequence}{/sequence}][{sequence floor=3, from=9007199254740993, rows=3}{$sequence} {/sequence}][{sequence modulo=10, from=9007199254740993, rows=3}{$sequence} {/sequence}][{sequence modulo=7, from=-9223372036854775808, rows=2}{$sequence} {/sequence}]

d[{sequence floor=-2, rows=5}{$sequence} {/sequence}] c[{sequence ceil=-2, rows=5}{$sequence} {/sequence}] m[{sequence '1..5', make, floor=-2}{$sequence} {/sequence}] n[{sequence '-5..-1', make, ceil=-2}{$sequence} {/sequence}] k[{sequence '1..10', keep, multiple=-3}{$sequence} {/sequence}] s[{sequence '1..4', make, step=-2}{$sequence} {/sequence}]

{sequence ceil=0.5, from=1, to=3}
  {$sequence},
{/sequence}

[{sequence modulo=3, from=-3, rows=4}{$sequence} {/sequence}][{sequence ceil=3, from=-2, rows=3}{$sequence} {/sequence}][{sequence round=3, from=-1, rows=2}{$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}";

?>