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PAD Sequence Types

This document describes the sequence types available in PAD and how to generate them.

Basic Sequence Generation

{fibonacci rows=10}{$fibonacci} {/fibonacci}      # Fibonacci numbers
{prime rows=15}{$prime} {/prime}                  # Prime numbers
{sequence '1..10', name='n'}{$n} {/sequence}      # Range 1-10
{random minimal=1, maximal=100, rows=5}           # Random numbers
{list '5;2;8;1;9'}{$list} {/list}                 # Custom list

Character/Letter Ranges

{sequence 'A..Z', name='letter'}{$letter} {/sequence}   # Full alphabet
{sequence 'a..e', name='c'}{$c} {/sequence}             # a, b, c, d, e
{sequence '0..9', name='digit'}{$digit} {/sequence}     # Digits as strings

OEIS Integration (Online Encyclopedia of Integer Sequences)

{sequence 10, oeis=81}{$sequence} {/sequence}           # OEIS sequence A000081
{sequence 15, oeis=257360}{$sequence} {/sequence}       # OEIS sequence A257360

Loop with from/to Parameters

{sequence loop, from=11, to=30, name='i'}{$i} {/sequence}

Sequence Types (80+)

Mathematical Sequences

fibonacci - Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, …)
lucas - Lucas numbers (2, 1, 3, 4, 7, 11, 18, …)
pell - Pell numbers (0, 1, 2, 5, 12, 29, …)
tribonacci - Tribonacci numbers (0, 0, 1, 1, 2, 4, 7, …)
catalan - Catalan numbers (1, 1, 2, 5, 14, 42, …)
bell - Bell numbers (1, 1, 2, 5, 15, 52, …)
perrin - Perrin numbers (3, 0, 2, 3, 2, 5, …)

prime - Prime numbers (2, 3, 5, 7, 11, 13, …)
composite - Composite numbers (4, 6, 8, 9, 10, …)
perfect - Perfect numbers (6, 28, 496, …)
mersenne - Mersenne numbers (3, 7, 31, 127, …)
emirp - Emirp primes (primes that are different primes when reversed)
strong - Strong primes
semiprime - Semiprimes (products of exactly two primes)

Figurate Numbers

triangular - Triangular numbers (1, 3, 6, 10, 15, …)
square - Square numbers (1, 4, 9, 16, 25, …)
cubic - Cubic numbers (1, 8, 27, 64, 125, …)
pentagonal - Pentagonal numbers (1, 5, 12, 22, 35, …)
hexagonal - Hexagonal numbers (1, 6, 15, 28, 45, …)
heptagonal - Heptagonal numbers (1, 7, 18, 34, 55, …)
octagonal - Octagonal numbers (1, 8, 21, 40, 65, …)
decagonal - Decagonal numbers
tetrahedral - Tetrahedral numbers (1, 4, 10, 20, 35, …)
octahedral - Octahedral numbers (1, 6, 19, 44, 85, …)
biquadratic - Biquadratic numbers (1, 16, 81, 256, …)
gnomonic - Gnomonic numbers (1, 3, 5, 7, 9, …)
pronic - Pronic/oblong numbers (n*(n+1))
heptadecagonal - Heptadecagonal numbers
enneadecagonal - Enneadecagonal numbers
icosihenagonal - Icosihenagonal numbers

Filters

even - Even numbers (2, 4, 6, 8, 10, …)
odd - Odd numbers (1, 3, 5, 7, 9, …)
happy - Happy numbers (1, 7, 10, 13, 19, …)
lucky - Lucky numbers (1, 3, 7, 9, 13, …)
harshad - Harshad/Niven numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, …)
palindrome - Palindromic numbers (1, 2, …, 9, 11, 22, …)
powerful - Powerful numbers (1, 4, 8, 9, 16, …)
polite - Polite numbers (3, 5, 6, 7, 9, …)
kaprekar - Kaprekar numbers (1, 9, 45, 55, …)
antiprime - Antiprime (highly composite) numbers

Other Sequences

golomb - Golomb sequence
gould - Gould sequence
kolakoski - Kolakoski sequence
kynea - Kynea numbers
moserdebruijn - Moser-de Bruijn sequence
newmanConway - Newman-Conway sequence
recaman - Recaman sequence
sylvester - Sylvester sequence
cullen - Cullen numbers
xpadovan - Padovan sequence
caterer - Lazy caterer’s sequence

Arithmetic Operations

add - Addition
subtract - Subtraction
multiply - Multiplication
divide - Division
modulo - Modulo operation
power / exponentiation - Power/exponentiation
ceil - Ceiling function
floor - Floor function
round - Rounding
negation - Negation

Logical Operations

and - Logical AND
or - Logical OR
xor - Logical XOR
not - Logical NOT
nand - Logical NAND
nor - Logical NOR
xnor - Logical XNOR

Generation

range - Range (e.g., '1..10')
list - Custom list (e.g., '1;5;3;8')
loop - Loop iteration
random - Random numbers
repeat - Repeat a value
oeis - Fetch from Online Encyclopedia of Integer Sequences
identity - Identity sequence (returns input)
step - Step sequence
chance - Chance/probability sequence

Storing and Retrieving Sequences

IMPORTANT: Store names cannot be the same as action names (e.g., can’t use push='first' because first is an action).

{sequence '1..10', push='mySeq'}           # Store sequence
{pull:mySeq}{$sequence} {/pull:mySeq}      # Retrieve and iterate

# Use pull: prefix to avoid naming conflicts with app tags
{sequence 5, push='nums'}
{pull:nums} {$sequence} {/pull:nums}

Sequence Tags

The sequence tags (resume, pull, keep, remove, flag, make) operate on stored sequences:

{sequence 5, push='mySeq'}           # Create and store sequence
{resume add=10}                       # Transform: add 10 to each value
{resume reverse}                      # Transform: reverse order
{pull:mySeq} {$sequence} {/pull:mySeq}  # Iterate stored sequence

Note: {resume} applies transformations to stored sequences. Use {continue} for skipping iterations (like PHP’s continue).

Sequence Variable Access

Use named sequences instead of level-based $-1 syntax:

{sequence 5, name='n'}
  {$n}                    # Correct - use named variable
{/sequence}

{sequence 5}
  {$-1}                   # Avoid - level-based access can be fragile
{/sequence}

Named vs Unnamed Sequences

Always prefer named sequences for clarity:

{sequence 5, name='i'}
  {$i}                  # Clear, explicit
{/sequence}

{sequence '1..3', name='row'}
  {sequence '1..4', name='col'}
    ({$row},{$col})
  {/sequence}
{/sequence}

Special Syntax Rules

Some sequences need sequence: prefix:

{sequence:repeat 42, rows=5}{$repeat}{/sequence:repeat}
{sequence:even rows=10}{$even}{/sequence:even}

Chance sequence needs a numeric parameter:

{chance 4, rows=15}    # 1-in-4 chance (not {chance rows=15})

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