Sequences - Xref - Sequences - prime

<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>

{if sequence:prime(8) eq 19}
  y
{/if}

<?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;

?>

[{echo sequence:prime(0)}][{echo sequence:fibonacci(-3)}][{echo sequence:fibonacci(2.7)}][{echo sequence:prime(1)}]

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

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

{sequence:prime rows=3}
  {$sequence},
{/sequence:prime}

<?php

  $n = 0;
  $m = 3;

?>

[{sequence $n}{$sequence} {/sequence}][{sequence prime, rows=0}{$sequence} {/sequence}][{loop0}x{/loop}][{sequence $m}{$sequence} {/sequence}]

[{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}]

[{set $n = 10 ** 30}{sequence prime, rows=$n, to=20}{$sequence} {/sequence}][{set $m = 0 - 10 ** 30}{sequence prime, rows=$m, to=20}{$sequence} {/sequence}][{sequence prime, rows='1e30', to=20}{$sequence} {/sequence}]

{sequence '11..16', push='nums'/}[{reverse 'prime'}{$sequence} {/reverse}][{action:first 'prime'}{$sequence} {/action:first}][{action:splice 'nums', splice=2}{$sequence} {/action:splice}][{append 5}{$sequence} {/append}][{action:sort 'nums'}{$sequence} {/action:sort}][{action:shift 'nums', shift=2}{$sequence} {/action:shift}]

[{echo sequence:prime(78499)}][{echo sequence:prime(100000)}][{echo sequence:square(500000)}][{echo sequence:totient(300000)}][{echo sequence:polite(999990)}][{echo sequence:prime(1229)}][{echo sequence:recaman(12)}][{echo sequence:bell(3)}]

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

{sequence '1..9', push='a'/}[{pull:a first, 2}{$sequence} {/pull:a}][{pull:a add, 2}{$sequence} {/pull:a}][{sequence '1..3', add, 2}{$sequence} {/sequence}][{sequence '1..3', first, 2}{$sequence} {/sequence}][{prime first, 3}{$sequence} {/prime}][{sequence add, 3, rows=3}{$sequence} {/sequence}]