Sequences - Xref - Options - from

<p>{sequence '1..8'}{$sequence} {/sequence}</p>
<p>{sequence fibonacci, rows=8}{$sequence} {/sequence}</p>
<p>{sequence prime, from=10, rows=6}{$sequence} {/sequence}</p>
<p>{sequence 'A..F'}{$sequence} {/sequence}</p>

{meta title='Sequences'}

<p>The <code>{sequence}</code> tag generates values instead of reading them: a
range, a mathematical series, letters - 122 types, each iterated like any data
tag:</p>

{example 'fragments/sequences_1'}

<p>That is the smallest corner of a whole subsystem: plays that keep, remove or flag terms,
stores that pass a sequence from one tag to the next, actions that transform it, and random
draws with their own rules. It has an application of its own, which is its manual:</p>

<p><b><a href="{$padHost}sequence/">The sequence application</a></b> - every type, play,
action and option, demonstrated live.</p>
<h2>Seeing and hearing them</h2>

<p>A sequence is data like any other, so {tag 'chart'} and {tag 'sparkline'} draw it
straight away with <code>sequence=</code>:</p>

{example 'fragments/sequences_2'}

<p>The sequence application has three pages built on that: the
<a href="{$padHost}sequence/?gallery">Gallery</a> draws every type beside the OEIS entry its
terms come from, <a href="{$padHost}sequence/?listen">Listen</a> plays a sequence as notes -
Recamán's is the famous one - in an audio file written into the page, and
<a href="{$padHost}sequence/?guess">Guess</a> shows the start of a sequence and asks for the
next term.</p>

<?php

  // The lenient walk under test: with the syntax check off, what cannot run passes the
  // value through or yields empty, and the walk carries on.

  $padCheckSyntax = FALSE;

?>

[{sequence '1;2;3', from='abc'}{$sequence} {/sequence}][{sequence 3, increment='x'}{$sequence} {/sequence}][{sequence 3, skip='x'}{$sequence} {/sequence}][{sequence 3, minimal='x'}{$sequence} {/sequence}][{sequence prime, to='x', rows=3}{$sequence} {/sequence}]

<?php

  // The lenient walk under test: with the syntax check off, what cannot run passes the
  // value through or yields empty, and the walk carries on.

  $padCheckSyntax = FALSE;

?>

[{sequence lucky, from=9223372036854775800, rows=2}{$sequence} @else@none{/sequence}][{sequence '1999999;2000029;9', flag, lucky}{$sequence}{/sequence}]

{code}{prime:keep rows=3, from=10}{$sequence},{/prime:keep}{/code}

{keep:prime rows=4, from=10}
  {$sequence},
{/keep:prime}

[{sequence multiple, from=9223372036854775800, rows=3}{$sequence} {/sequence}][{sequence '9223372036854775800;5', make, multiple}{$sequence} {/sequence}]

[{sequence pentagonal, from=-2, rows=3}{$sequence} {/sequence}][{sequence polite, from=-1, rows=3}{$sequence} {/sequence}][{sequence pell, from=-2, rows=3}{$sequence} {/sequence}][{sequence gnomonic, from=-1, rows=3}{$sequence} {/sequence}][{sequence tetrahedral, from=-2, rows=3}{$sequence} {/sequence}][{sequence octahedral, from=-1, rows=3}{$sequence} {/sequence}][{sequence '-2..2', make, hexagonal}{$sequence} {/sequence}][{sequence decagonal, from=1.5, rows=2}{$sequence} {/sequence}]

[{echo sequence:square(2000000)}][{echo sequence:pentagonal(1000001)}][{echo sequence:cubic(2000000)}][{echo sequence:square(5)}][{sequence emirp, build='function', from=3, rows=2}{$sequence} {/sequence}][{sequence multiple=3, build='function', from=2, rows=3}{$sequence} {/sequence}][{sequence golomb, build='function', rows=5}{$sequence} {/sequence}][{sequence pentagonal, build='function', from=3, rows=2}{$sequence} {/sequence}][{sequence cullen, from=56, rows=4}{$sequence} {/sequence}][{sequence '0..3', make, kynea}{$sequence} {/sequence}]

[{sequence newmanConway, from=3.0, rows=2}{$sequence} {/sequence}][{sequence newmanConway, from='+3', rows=2}{$sequence} {/sequence}][{sequence bell, from=3.0, rows=2}{$sequence} {/sequence}][{sequence '3.0;+3;3e0', make='newmanConway'}{$sequence} {/sequence}][{sequence '3.0;+3;3e0', make='bell'}{$sequence} {/sequence}][{sequence '4;4.0', make, bell, flag, odd}{$sequence} {/sequence}]

[{sequence lucky, from=1999990, rows=3}{$sequence} @else@none{/sequence}][{sequence from=1999999, rows=3, flag='lucky'}{$sequence}{/sequence}]

<?php

  // A ceiling of 50,000 candidates: strong's fourth term, 40585, stands within it, and the walk
  // that goes on from it for a fifth has what is left of the candidates and comes up short.

  $padSeqMaxTries = 50000;

?>

[{sequence '1..6', make, strong, build='order'}{$sequence} {/sequence}][{sequence '5;1;9;3;12', make, happy, build='order'}{$sequence} {/sequence}][{sequence '3;1;8;2;20', make, lucky, build='order'}{$sequence} {/sequence}][{sequence '1;2;1;3;4;5', make, strong, build='function'}{$sequence} {/sequence}][{sequence harshad, build='function', from=9, rows=4}{$sequence} {/sequence}][{sequence '1..6', make, amicable, build='order'}{$sequence} {/sequence}][{sequence amicable, build='function', from=3, rows=4}{$sequence} {/sequence}]

{sequence '-10..10', keep='prime'}{$sequence} {/sequence}|{sequence prime, from=-5, rows=3}{$sequence} {/sequence}

{sequence loop, from=6, rows=8, remove='power|2'}
  {$sequence},
{/sequence}

{sequence loop, from=0, rows=4, keep='power|2'}
  {$sequence},
{/sequence}