> ## Documentation Index
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# Bash Zero-padded Sequence
A zero-padded sequence is a specific form of Bash brace expansion that generates a contiguous range of integers formatted with leading zeros to enforce a uniform string width. Introduced in Bash 4.0, the expansion engine evaluates the maximum character width of the specified boundaries and pads all generated elements to match that width.
## Syntax
```bash theme={"dark"}
# Basic zero-padded sequence
{0START..END}
{START..0END}
# Zero-padded sequence with a step increment
{0START..0END..INCREMENT}
```
## Evaluation Mechanics
* **Width Determination:** The total width of every element in the generated sequence is dictated by the boundary parameter (`START` or `END`) with the greatest number of characters. To trigger the padding behavior, the absolute value of either boundary must be prefixed with a `0` (e.g., `05` or `-05`).
* **Textual Expansion vs. Arithmetic:** Brace expansion is a textual/string expansion that occurs *before* arithmetic evaluation. Consequently, leading zeros in brace expansion denote formatting width, not octal numbers. For example, `{01..010}` expands up to base-10 `10`, whereas an actual arithmetic operation like `$((010))` evaluates to base-10 `8`.
* **Negative Integers:** When generating sequences that include negative numbers, the minus sign (`-`) is calculated as part of the total string width. The zero-padding is inserted strictly between the minus sign and the integer.
* **Order of Expansion:** Brace expansion is the very first step in the Bash shell expansion process. It occurs strictly before parameter and variable expansion. Consequently, variables cannot be used to define the `START`, `END`, or `INCREMENT` values dynamically without utilizing `eval`.
* **Type Restriction:** Zero-padding applies exclusively to integer sequences. It cannot be used with alphabetic character sequences. Because Bash requires alphabetic sequence boundaries to be exactly one character long, prefixing a character with a zero (e.g., `{0a..z}`) fundamentally breaks the sequence syntax. The expansion engine rejects it entirely, leaving the expression as an unexpanded literal string.
## Syntax Visualization
**Standard Padding:**
The width is determined by `005` (3 characters). The starting integer `1` is padded to `001`.
```bash theme={"dark"}
$ echo {001..005}
001 002 003 004 005
```
**Asymmetric Padding Definition:**
Only one boundary requires the zero prefix to trigger the behavior. The longest string (`010`) sets the width to 3.
```bash theme={"dark"}
$ echo {1..010}
001 002 003 004 005 006 007 008 009 010
```
**Stepped Increment:**
Generates a sequence from 0 to 15, incrementing by 5, padded to a width of 2.
```bash theme={"dark"}
$ echo {00..15..5}
00 05 10 15
```
**Negative Integer Padding:**
The width is determined by `-05` (3 characters). Positive numbers in the sequence are padded to 3 characters, while negative numbers use one character for the minus sign and are padded to fill the remaining two characters.
```bash theme={"dark"}
$ echo {-05..05..5}
-05 000 005
```
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