Left-Shifted Odd Number Triangle Pattern in PHP

Beginner

⏱️ 8 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Step Size Loop

Left-shifted odd number triangle output (13579, 3579, 579, 79, 9) in PHP programming

Overview

What You’ll Learn

The left-shifted odd number triangle prints consecutive odd digits on each row while the starting odd value increases — a great exercise in nested loops with step size 2. This tutorial covers the shape rule, loop structure, a live preview, algorithm steps, worked PHP examples, edge cases, and complexity.

Shape Rule

Odd numbers only

Row 1 prints 13579, row 2 prints 3579, row 3 prints 579, and so on as the start shifts right.

Outer Loop

i += 2

for ($i = 1; $i <= $max; $i += 2) picks the starting odd number for each row: 1, 3, 5, 7, 9.

Inner Loop

j += 2 to max

for ($j = $i; $j <= $max; $j += 2) prints odd digits from the row start up to $max.

echo vs PHP_EOL

Same line / next line

Odd digits use echo $j; end each row with echo PHP_EOL.

Live Preview

1–20 max

Pick a maximum value and draw the left-shifted odd triangle instantly in the browser.

O(n²)

Complexity

Total digit prints shrink each row; complexity is still O(n²) for maximum n.

Introduction

A left-shifted odd number triangle prints consecutive odd numbers on each row while the starting odd value increases by 2. With max = 10, the output is 13579, 3579, 579, 79, 9.

In PHP you solve it with nested loops that step by 2: for ($i = 1; $i <= $max; $i += 2) and for ($j = $i; $j <= $max; $j += 2), then echo PHP_EOL; ends each row.

Why it matters?

It teaches step-size loops (+= 2) before more complex parity-based patterns.

Key Highlights

Step Size 2

i += 2 and j += 2 visit only odd values.

Left Shift

Each row starts at a larger odd i, so fewer digits print.

Print Then Break

echo $j in the inner loop; echo PHP_EOL after.

Series Foundation

Follow Program 16; continue to Program 18 (alternating odd/even rows).

In short: for each odd start i from 1 to max, print odd j from i to max stepping by 2, then call echo PHP_EOL.

Foundation

📝 Problem & Approach

Given a positive integer max, print a left-shifted odd number triangle: row starting at odd i prints odd digits from i to max stepping by 2.

PHP

// max = 10 (conceptual shape)
// 13579
// 3579
// 579
// 79
// 9

Inputs & Outputs

Item	Type	Description
`max`	int	Upper bound for odd digits on each row (typically ≥ 1).
Printed output	text	Each row prints consecutive odd numbers from `i` to `max`.

Minimal workflow

Pseudocode

for i from 1 to max step 2:
    for j from i to max step 2:
        print j (no newline)
    print newline

Approach comparison

Approach	Idea	Best for
Nested loops + step 2	13579, 3579, …	Learning and interviews
Even max adjustment	`if ($max % 2 === 0) $max -= 1;`	User-input programs
Even-number variant	Start at 2 with `+= 2`	Mirror pattern with evens

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Walk each row start	`for ($i = 1; $i <= $max; $i += 2)`
Print odd digit	`for ($j = $i; $j <= $max; $j += 2) echo $j;`
End the row	`echo PHP_EOL;`
Force odd maximum	`if ($max % 2 === 0) $max -= 1;`
Even variant	`for ($i = 2; $i <= $max; $i += 2)` with `$j = $i` to `$max`
Spaced output	`echo $j;`

Compare

📋 Step 2 vs Even Max vs Even Variant

Same left-shift idea — different bounds and step handling.

i += 2

odd start

Outer loop picks 1, 3, 5, 7, 9

j += 2

odd digits

Inner loop prints only odd values

max -= 1

even fix

Adjust even user input to odd bound

Learning tip

trace i,j

Trace max = 10 on paper before coding

Context

When This Pattern Shows Up

Reach for this pattern when teaching loop step sizes and shrinking row widths.

First lab exercise
Step-size loops build on binary patterns from Programs 15 and 16.
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with fgets(STDIN) for a flexible row count.
Gateway to variants
Compare Program 16 (binary triangle) and Program 18 (alternating odd/even rows) next.
Not a UI layout tool
This is a console teaching pattern — not how you build modern app screens.

Key benefit: one small program that locks in nested loops, output sequencing, and O(n²) thinking.

Interactive

🔮 Live Preview

Choose a maximum between 1 and 20 and draw the left-shifted odd triangle in the browser.

Hands-On

Examples Gallery

Three complete PHP programs — fixed maximum, user input, and an even-number mirror variant. Click View Output to reveal sample console results.

📚 Getting Started

Print the left-shifted odd triangle with max = 10 and += 2 loops.

Example 1 — Fixed `max = 10`

Hard-coded upper bound — ideal for first demos and screenshots.

PHP

<?php
for ($i = 1; $i <= 10; $i += 2) {
    for ($j = $i; $j <= 10; $j += 2) {
        echo $j;
    }
    echo PHP_EOL;
}

How It Works

When i = 1, the inner loop prints 1, 3, 5, 7, 9 as 13579. When i = 5, it prints 5, 7, 9 as 579, and so on as the start shifts right. echo PHP_EOL after the inner loop starts the next row.

📈 User Input

Read the maximum with fgets(STDIN) and adjust even input to an odd bound.

Example 2 — User Input Version

Read max with (int) trim(fgets(STDIN)); subtract 1 when the value is even.

PHP

<?php
echo "Enter the maximum value: ";
$max = (int) trim(fgets(STDIN));

if ($max % 2 === 0) $max -= 1;

for ($i = 1; $i <= $max; $i += 2) {
    for ($j = $i; $j <= $max; $j += 2) {
        echo $j;
    }
    echo PHP_EOL;
}

How It Works

max = 8 becomes 7 after the even adjustment, so the last odd printed is 7. The nested += 2 loops stay the same as Example 1. Non-numeric input leaves max unset if you skip is_numeric() checks — always check it in safer labs.

⚡ Even Variant

Mirror the pattern with even numbers starting at 2 instead of 1.

Example 3 — Even Number Mirror

Start both loops at 2 and step by 2 to print only even digits up to max = 10.

PHP

<?php
$max = 10;

for ($i = 2; $i <= $max; $i += 2) {
    for ($j = $i; $j <= $max; $j += 2) {
        echo $j;
    }
    echo PHP_EOL;
}

How It Works

Same left-shift structure as Example 1, but both loops start at 2 and visit only even values. Compare with the odd version to see how the start value changes the sequence.

🧠 How the Algorithm Prints Rows

Set up

Set $max = 10; and use fgets(STDIN) when reading input. Set max (fixed or from input).

Setup

Outer loop (row start)

for ($i = 1; $i <= $max; $i += 2) picks the starting odd number: 1, 3, 5, 7, 9.

Row

Inner loop (odd digits)

for ($j = $i; $j <= $max; $j += 2) prints each odd value with echo $j.

Odd-only

New line

echo PHP_EOL ends the row so the next outer iteration starts fresh.

Break

Left-shifted triangle complete

Each row prints fewer digits as i grows — O(n²) time for maximum n, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `max = 10`

Trace each outer-loop value of i and note the odd j values printed on each row.

`i`	Inner `j` values	Printed row
`1`	`1, 3, 5, 7, 9`	`13579`
`3`	`3, 5, 7, 9`	`3579`
`5`	`5, 7, 9`	`579`
`7`	`7, 9`	`79`
`9`	`9`	`9`

Five rows for max = 10; digit count shrinks from 5 down to 1.

Use Cases

Where this tiny pattern (and its loop structure) shows up beyond the homework prompt.

1. Teaching Nested Loops

Clearest visual proof that outer and inner bounds interact.

Example: change j <= i and watch the shape change.

2. Pattern Series Base

Foundation for inverted, pyramid, diamond, and hollow variants.

Example: use (i + j) % 2 for row+column parity grids.

3. Console Formatting Drills

Practice echo vs PHP_EOL without complex math.

Example: put echo PHP_EOL inside the inner loop by mistake.

4. Character Substitution

Swap digits for letters, stars, or spaced output once the loop works.

Example: print j + " " for spaced digits on each row.

5. Complexity Intuition

Triangular totals make O(n²) concrete for beginners.

Example: count printed digits for n = 10 still → 55.

6. Input Validation Labs

Pair the pattern with fgets(STDIN) and is_numeric() checks and positive-row checks.

Example: reject max <= 0 and re-prompt.

Pro Tip: when an interviewer asks for patterns, explain the outer/inner roles first — then write the loops. The story matters as much as the code.

Advantages

Why this pattern earns a permanent spot in beginner C courses.

1. Instant Visual Feedback
Wrong bounds show up immediately as a broken staircase.
2. Minimal Concepts
Only loops and console output — no arrays or math libraries.
3. Easy to Extend
Invert, center, hollow, or change the fill character with small edits.
4. O(1) Extra Memory
Streaming output needs no storage beyond loop counters.

Pro Tip: learn += 2 first; compare with j++ to see how step size changes which numbers print.

Usage Tips

Small habits that keep number-pattern code clean.

1. Name Bounds Clearly
Use max (or n) and keep i/j for row/column — or rename to start/value.
2. Validate CLI input
Call is_numeric(trim($line)) so bad input does not leave max uninitialized.
3. Keep echo PHP_EOL Outside
Only call echo PHP_EOL after the inner loop finishes the row.
4. Force Odd Maximum
if ($max % 2 === 0) $max -= 1; keeps the bound odd when reading input.
5. Dry-Run One Small n
Trace max = 10 on paper before coding larger demos.

Pro Tip: if the output is a vertical list of single digits per line, you almost certainly put echo PHP_EOL inside the inner loop.

Common Pitfalls

Mistakes that commonly break left-shifted odd number patterns.

1. Newline Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use echo $j for digits; echo PHP_EOL only after the inner loop.
2. Using j++ Instead of j += 2
j++ prints even numbers too — the row no longer contains only odds.
→ For odd-only rows, keep for ($j = $i; $j <= $max; $j += 2).
3. Forgetting the Row Break
Omitting echo PHP_EOL glues every digit onto one endless line.
→ Always end the row after the inner loop.
4. Unchecked CLI input
Letters or empty input leave max uninitialized.
→ Prefer is_numeric() and re-prompt on failure.
5. Off-by-One on 0-Based Loops
Switching to i = 0 without adjusting the inner bound prints an empty first row or wrong counts.
→ If 0-based, print i with wrong inner bound (e.g. j <= i + 1).

Edge Cases

Check these inputs before calling the solution done.

max = 1

Single digit

Output is just 1 on one line.

max = 0

Empty pattern

Outer loop never runs — print nothing or show a message.

Negative

`max < 0`

Treat as invalid; re-prompt instead of silent empty output.

Large n

Many rows

Output grows as n²/2 characters — fine for labs, noisy for huge n.

Bad input

Non-numeric CLI input

Unchecked fgets(STDIN) leaves max unset — call is_numeric(trim($line)) first.

Even max

Even maximum input

Subtract 1 or prompt again — otherwise the last odd may not match intent.

j++

Wrong step size

j++ includes even numbers — use j += 2 for odd-only output.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Ascending binary triangle

Inner loop j = 1 to i with j % 2
Continue with Program 16

2. Alternating odd/even rows

Switch start value by row parity
Continue with Program 18

3. Even mirror pattern

Start at 2 with += 2 on both loops
Compare output with Example 3

4. Spaced odd output

Use echo $j between digits
Harder follow-up after this page

Important

Notes

Shrinking rows. Digit count per row decreases as i grows — still O(n²) prints for maximum n.
echo $j stays on the line; echo PHP_EOL advances — mix them carefully.
Validate max > 0 for interactive programs; max = 1 should print a single 1.
This page is left-aligned. Centered pyramids need leading spaces — covered later in the series.

Quick Takeaway: outer loop steps by 2 for row starts, inner loop prints odd j up to max, then break the line.

Analysis

⏱️ Time and Space Complexity

Program	Time	Extra space
Nested loops (Examples 1–2)	`O(max²)`	`O(1)`
Even variant (Example 3)	`O(max²)`	`O(1)`

Wrap Up

🎉 Conclusion

The left-shifted odd number triangle is a compact lesson in loop step sizes: += 2 on both loops prints only odd values while each row starts later. Master the fixed-max version, then try the user-input and even-mirror variants.

Practice the three examples above, then continue to Program 18 for the alternating odd/even number triangle.

Use $i += 2 and $j += 2 for odd-only digits — keep echo for numbers and echo PHP_EOL; for the break, and adjust even $max when reading input.

View Examples Gallery Continue to Program 18

Pro Tips

💡 Best Practices

✅ Do

Explain i += 2 and j += 2 before coding
Use echo $j for digits and echo PHP_EOL after each row
Validate max ≥ 1 for interactive programs
Call is_numeric(trim($line)) before using max
State O(n²) time when asked about complexity

❌ Don’t

Call echo PHP_EOL inside the inner digit loop
Use j++ when you meant odd-only with j += 2
Skip the newline after each row
Ignore bad console input in user-facing demos
Skip the max = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this left-shifted pattern

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

Only odd digits print

Definition

↻ 02

Outer loop

i += 2 picks start

Code

% 03

Inner loop

j += 2 to max

Code

← 04

Left shift

Rows shrink each line

Shape

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why does the output contain only odd numbers?

Both loops increment by 2 ($i += 2 and $j += 2), so they visit only odd values: 1, 3, 5, 7, 9.

Why does the pattern shift left on each row?

Each next row starts from a larger odd number ($i increases by 2), so fewer digits print on that row.

Why does the last row print only 9?

On the last iteration, $i = 9, so the inner loop prints only 9 once.

What is the difference between echo and PHP_EOL?

echo $j stays on the same line. echo PHP_EOL ends the current line. Digits use echo; the row break uses echo PHP_EOL after the inner loop.

Can I include 10 in the output?

Not with += 2 starting from odd numbers — that visits only odd values. To include 10, use $j++ or handle even values separately.

What if the user enters an even maximum?

Subtract 1 ($max -= 1) so the last printed odd matches the intended width, as shown in Example 2.

What is the time complexity?

O(n²) for maximum value n. Only about half the numbers are visited due to step size 2, but nested loops still dominate.

How should I read the maximum safely?

Use trim(fgets(STDIN)) and check is_numeric($input) before casting to int so bad input does not produce unexpected results.

What happens if max is 0 or negative?

The outer loop never runs, so nothing is printed. Validate and prompt again if you want a clear user message.

Did you Know? 🔊

Both loops step by 2 with $i += 2 and $j += 2, so only odd numbers print. Each row starts at a larger odd value, so the triangle shifts left — still O(n²) for maximum n.

Continue to Program 18

Move on to the alternating odd/even number triangle in the PHP number-pattern series.

Program 18 tutorial →

About the author

Mari Selvan M P 🔗

Developer, cloud engineer, and technical writer

Experience 12 years building web and cloud systems
Focus Full Stack Development, AWS, and Developer Education

I write practical tutorials so students and working developers can learn by doing—from databases and APIs to deployment on AWS.

AWS Certified Developer – Associate (Credly)

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PHP Number Pattern 16 — Column-Wise Alternating Binary PHP Number Pattern 18 — Alternating Odd/Even Triangle

Left-Shifted Odd Number Triangle Pattern in PHP

What You’ll Learn

Shape Rule

Outer Loop

Inner Loop

echo vs PHP_EOL

Live Preview

O(n²)

Introduction

Why it matters?

Step Size 2

Left Shift

Print Then Break

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 Step 2 vs Even Max vs Even Variant

When This Pattern Shows Up

First lab exercise

Nested-loop warm-up

Console I/O practice

Gateway to variants

Not a UI layout tool

🔮 Live Preview

Examples Gallery

📚 Getting Started

Example 1 — Fixed max = 10

How It Works

📈 User Input

Example 2 — User Input Version

How It Works

⚡ Even Variant

Example 3 — Even Number Mirror

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop (row start)

Inner loop (odd digits)

New line

Left-shifted triangle complete

🔎 Worked Walkthrough — max = 10

Use Cases

1. Teaching Nested Loops

2. Pattern Series Base

3. Console Formatting Drills

4. Character Substitution

5. Complexity Intuition

6. Input Validation Labs

Advantages

1. Instant Visual Feedback

2. Minimal Concepts

3. Easy to Extend

4. O(1) Extra Memory

Usage Tips

1. Name Bounds Clearly

2. Validate CLI input

3. Keep echo PHP_EOL Outside

4. Force Odd Maximum

5. Dry-Run One Small n

Common Pitfalls

1. Newline Inside the Inner Loop

2. Using j++ Instead of j += 2

3. Forgetting the Row Break

4. Unchecked CLI input

5. Off-by-One on 0-Based Loops

Edge Cases

Single digit

Empty pattern

max < 0

Many rows

Non-numeric CLI input

Even maximum input

Wrong step size

🎯 Practice Problems

1. Ascending binary triangle

2. Alternating odd/even rows

3. Even mirror pattern

Example 1 — Fixed `max = 10`

🔎 Worked Walkthrough — `max = 10`

`max < 0`