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

PHP
HTML
fragments/sequences_1.pad 		Result 
<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>

1 2 3 4 5 6 7 8

0 1 1 2 3 5 8 13

11 13 17 19 23 29

A B C D E F

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:

The sequence application - every type, play, action and option, demonstrated live.

Seeing and hearing them

A sequence is data like any other, so {chart} and {sparkline} draw it straight away with sequence=:

PHP
HTML
fragments/sequences_2.pad 		Result 
<p>Primes: {sparkline sequence='prime', rows=20}</p>
<p>Recamán: {sparkline sequence='recaman', rows=40, width=200}</p>

Primes: Prime, the first 20 terms1: 2; 2: 3; 3: 5; 4: 7; 5: 11; 6: 13; 7: 17; 8: 19; 9: 23; 10: 29; 11: 31; 12: 37; 13: 41; 14: 43; 15: 47; 16: 53; 17: 59; 18: 61; 19: 67; 20: 71

Recamán: Recaman, the first 40 terms1: 0; 2: 1; 3: 3; 4: 6; 5: 2; 6: 7; 7: 13; 8: 20; 9: 12; 10: 21; 11: 11; 12: 22; 13: 10; 14: 23; 15: 9; 16: 24; 17: 8; 18: 25; 19: 43; 20: 62; 21: 42; 22: 63; 23: 41; 24: 18; 25: 42; 26: 17; 27: 43; 28: 16; 29: 44; 30: 15; 31: 45; 32: 14; 33: 46; 34: 79; 35: 113; 36: 78; 37: 114; 38: 77; 39: 39; 40: 78

The sequence application has three pages built on that: the Gallery draws every type beside the OEIS entry its terms come from, Listen plays a sequence as notes - Recamán's is the famous one - in an audio file written into the page, and Guess shows the start of a sequence and asks for the next term.