Increasing Odd-Length Number Rows in Python

Q: What if the user enters an even maximum?

Subtract 1 to make it odd (see Example 2) so the last row still has an odd length.

Q: What is the time complexity?

O(n²) for maximum row length n because total prints are 1+3+5+...+n.

Q: How should I read max_n safely?

Use a try/except ValueError around int(input()) or check the raw string with .isdigit() before converting so bad input does not crash the script.

Q: What happens if max_n is 0 or negative?

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

Beginner

⏱️ 7 min read

📚 Updated: Aug 2026

🎯 3 Code Examples

🚀 Live Preview

Step Size Loop

Increasing odd-length number rows output (1, 123, 12345, 1234567, 123456789) in Python programming

Overview

What You’ll Learn

The increasing odd-length number rows pattern uses range(..., 2) in the outer loop so each row prints 1..i with lengths 1, 3, 5, 7, 9 — a natural step after the jump triangle in Program 21. This tutorial covers the shape rule, step-size logic, a live preview, algorithm steps, worked Python examples, edge cases, and complexity.

Shape Rule

Odd row lengths

Row 1 prints 1, row 2 prints 123, row 3 prints 12345, and so on — digits run together with no spaces.

Outer Loop

i += 2

for i in range(1, max_n + 1, 2) walks odd values 1, 3, 5, 7, 9 as row lengths.

Inner Loop

1..i

for j in range(1, i + 1) then print(j, end="") — no space between digits.

print end= vs print()

Same line / next line

Digits use print(j, end=""); end each row with print().

Live Preview

1–15 max

Pick an odd maximum and draw the odd-length rows pattern instantly in the browser.

O(n²)

Complexity

Total prints = 1+3+5+...+max_n; extra memory stays O(1).

Introduction

An increasing odd-length number rows pattern prints consecutive digits 1..i on each row, with row lengths growing by 2 each time. With max_n = 9, the output is 1, 123, 12345, 1234567, 123456789.

In Python you use for i in range(1, max_n + 1, 2) in the outer loop and print(j, end="") in the inner loop, then print() ends each row.

Why it matters?

It introduces loop step sizes — a simple change to range(..., 2) creates a whole new family of patterns.

Key Highlights

Outer i += 2

Row lengths are 1, 3, 5, 7, 9 — always odd.

Inner 1..i

print(j, end="") concatenates digits on one line.

No spaces

Digits run together — 123 not 1 2 3.

Series Foundation

Follow Program 21; continue to Program 23 (number & asterisk mirror) next.

In short: for each odd i up to max_n, print digits 1 through i with print(j, end=""), then call print().

Foundation

📝 Problem & Approach

Given a positive odd integer max_n, print increasing odd-length rows: for each odd i from 1 to max_n, print digits 1 through i concatenated on one line.

Python

# max_n = 9 (conceptual shape)
# 1
# 123
# 12345
# 1234567
# 123456789

Inputs & Outputs

Item	Type	Description
`max_n`	int	Maximum row length (typically odd, e.g. 9).
`i`	int	Outer loop — odd values 1, 3, 5, … up to `max_n`.
`j`	int	Inner loop — prints digits 1 through `i`.
Printed output	text	Row `i` has `i` concatenated digits — no spaces.

Minimal workflow

Pseudocode

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

Approach comparison

Approach	Idea	Best for
Outer i += 2	1, 123, 12345, …	Learning and interviews
User-input max_n	`max_n = int(input(...))`	Flexible console programs
Inner j += 2	1, 13, 135, 1357, …	Odd-only digit rows

Cheat Sheet

⚡ Quick Reference

Goal	Pattern
Walk odd lengths	`for i in range(1, max_n + 1, 2)`
Print digits	`for j in range(1, i + 1)`
Write digit	`print(j, end="")`
End the row	`print()`
Odd-only variant	`for j in range(1, i + 1, 2)`
User input	`max_n = int(input(...))`

Compare

📋 Fixed Max vs User Input vs Odd-Only Digits

Same odd-length rows — different ways to control max_n and inner loop step.

Outer step

range step 2

Row lengths 1, 3, 5, 7, 9

Inner 1..i

print(j, end="")

Concatenate digits — no spaces

Odd digits

j step 2

Print 1, 3, 5 only in Example 3

Learning tip

even max_n

Subtract 1 if user enters an even maximum

Context

When This Pattern Shows Up

Reach for this pattern when teaching loop step sizes and concatenated digit output inside nested loops.

Post-jump exercise
Natural follow-up after Program 21 — introduces outer loop step range(..., 2).
Nested-loop warm-up
Outer/inner bound practice with an immediate visual check.
Console I/O practice
Combine loops with input() for a flexible row count.
Gateway to variants
Compare Program 21 (jump triangle) and Program 23 (number & asterisk mirror) 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 an odd maximum between 1 and 15 and draw the odd-length rows pattern in the browser.

Hands-On

Examples Gallery

Three complete Python programs — fixed maximum, user input, and odd-only digits variant. Click View Output to reveal sample console results.

📚 Getting Started

Print five rows of odd-length consecutive digits with outer range(..., 2).

Example 1 — Fixed `max_n = 9`

Hard-coded maximum — ideal for first demos and screenshots.

Python

for i in range(1, 10, 2):
    for j in range(1, i + 1):
        print(j, end="")
    print()

How It Works

When i = 1, the inner loop prints 1 once. When i = 3, j runs 1, 2, 3 — output 123. When i = 9, digits 1 through 9 concatenate into 123456789. print() after the inner loop starts the next row.

📈 User Input

Read the maximum with input() instead of hard-coding 9.

Example 2 — User Input

Read max_n with int(input()); adjust to odd if the user enters an even value.

Python

max_n = int(input("Enter the maximum value: "))

if max_n % 2 == 0:
    max_n -= 1

for i in range(1, max_n + 1, 2):
    for j in range(1, i + 1):
        print(j, end="")
    print()

How It Works

Same nested-loop core as Example 1; only the source of max_n changes. The if max_n % 2 == 0: max_n -= 1 guard keeps the last row odd-length. Non-numeric input raises ValueError from int(input()) — wrap it in try/except in safer labs.

⚡ Odd-Only Digits

Use step 2 in the inner range to print only odd digits.

Example 3 — Odd-Only Digits `range(..., 2)`

Keep max_n = 9 but print 1, 3, 5, 7, 9 instead of 1..i on each row.

Python

for i in range(1, 10, 2):
    for j in range(1, i + 1, 2):
        print(j, end="")
    print()

How It Works

Change only the inner loop to range(1, i + 1, 2) — the outer loop and print() logic stay the same. Each row prints odd digits up to i instead of every digit from 1 to i.

🧠 How the Algorithm Prints Rows

Set up

print is built in; use input() when reading input. Set max_n and loop variables i, j.

Setup

Outer loop + range step 2

for i in range(1, max_n + 1, 2) — row lengths are 1, 3, 5, 7, 9.

Row

Inner loop + print(j, end="")

for j in range(1, i + 1) then print(j, end="") — digits concatenate with no spaces.

Digits

New line

print() ends the row so the next outer iteration starts fresh.

Break

Odd-length rows complete

Total prints grow as 1+3+5+...+max_n — O(n²) time, O(1) extra memory.

Trace

🔎 Worked Walkthrough — `max_n = 9`

Trace each outer-loop value of i and the digits printed on each row.

`i`	Inner `j` range	Digits printed	Row output
`1`	1	`1`	`1`
`3`	1..3	`1, 2, 3`	`123`
`5`	1..5	`1, 2, 3, 4, 5`	`12345`
`7`	1..7	`1..7`	`1234567`
`9`	1..9	`1..9`	`123456789`

Total digit prints: 1 + 3 + 5 + 7 + 9 = 25.

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 print(..., end="") vs row newline without complex math.

Example: put print() 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 try/except ValueError and positive-max checks.

Example: reject max_n <= 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 Python 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 range(..., 2) in the outer loop first; compare with range(..., 2) odd-digit variant in Example 3.

Usage Tips

Small habits that keep number-pattern code clean.

1. Name Bounds Clearly
Use print(j, end="") without spaces — not print(j, end=" ") unless you want gaps.
2. Validate input()
Wrap int(input()) in try/except ValueError so bad input does not crash the script.
3. Keep print() Outside
Only call print() after the inner loop finishes the row.
4. Trace i and j on Paper
Write each odd i and the j range before coding.
5. Dry-Run One Small n
Trace max_n = 7 on paper before coding larger demos.

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

Common Pitfalls

Mistakes that commonly break odd-length row patterns.

1. Newline Inside the Inner Loop
Each digit lands on its own line — you get a column, not a triangle.
→ Use print(j, end=""); print() only after the inner loop.
2. Forgetting range step 2
Using step 1 (no step-2 range) prints every length 1, 2, 3, 4 — not odd lengths only.
→ Use for i in range(1, max_n + 1, 2) for odd row lengths.
3. Adding Spaces Between Digits
print(j, end=" ") produces 1 2 3 instead of 123.
→ Use print(j, end="") for concatenated digits.
4. Forgetting the Row Break
Omitting print() glues every number onto one endless line.
→ Always end the row after the inner loop.
5. Unchecked input
Letters or empty input raise ValueError from int(input()).
→ Wrap int(input()) in try/except ValueError and re-prompt on failure.

Edge Cases

Check these inputs before calling the solution done.

max_n = 1

Single digit

Output is just 1 on one line.

max_n = 0

Empty pattern

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

Negative

`max_n < 0`

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

Large n

Large width

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

Bad input

Non-numeric input

int(input()) raises ValueError — validate with try/except first.

Even max

User enters even

Subtract 1 to keep odd row lengths — see Example 2.

Drill

🎯 Practice Problems

Try these variations to lock in the pattern.

1. Jump number triangle

Decreasing step variable per row
Review Program 21

2. Number & asterisk mirror

Mirror pattern with stars
Continue with Program 23

3. Spaced digits

Use print(j, end=" ") for gaps
Compare with concatenated output

4. No trailing space

Print space only between numbers, not after the last
Harder follow-up after this page

Important

Notes

Odd sum. Total prints = 1+3+5+...+max_n — O(n²) for maximum row length n.
print(j, end="") stays on the line; print() advances — mix them carefully.
Validate max_n > 0 for interactive programs; max_n = 1 should print a single 1.
This page is left-aligned. Centered pyramids need leading spaces — covered later in the series.

Quick Takeaway: use range(..., 2) in the outer loop, print(j, end="") in the inner loop, then print() after each row.

Analysis

⏱️ Time and Space Complexity

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

Wrap Up

🎉 Conclusion

The increasing odd-length number rows pattern is a compact lesson in loop step sizes: use range(..., 2) in the outer loop and print(j, end="") in the inner loop to concatenate digits. Master the fixed-max version, then try user input and the odd-only digit variant.

Practice the three examples above, then continue to Program 23 for the number & asterisk mirror pattern.

Use range(..., 2) for odd lengths — validate max_n and adjust even input when reading from the console.

View Examples Gallery Continue to Program 23

Pro Tips

💡 Best Practices

✅ Do

Use for i in range(1, max_n + 1, 2) in the outer loop
Use print(j, end="") — no space between digits
Adjust even max_n with max_n -= 1 for user input
Wrap int(input()) in try/except ValueError before using max_n
State O(n²) time when asked about complexity

❌ Don’t

Call print() inside the inner digit loop
Use step 1 when you want odd lengths only
Add spaces unless you want separated digits
Skip the newline after each row
Ignore bad console input in user-facing demos
Skip the max_n = 1 edge case

Summary

Key Takeaways

Knowledge Unlocked

Five things to remember about this odd-length pattern

Print the pattern the beginner-friendly way.

Core concepts

△ 01

Rule

i += 2 rows

Definition

↻ 02

Inner 1..i

print(j, end="") no space

Code

+ 03

Odd lengths

1, 3, 5, 7, 9

Shape

↑ 04

j += 2

Odd digits variant

Variant

O 05

Complexity

O(n²) time

Analysis

❓ Frequently Asked Questions

Why does each row length increase by 2?

Because the outer loop uses range with step 2, so i becomes 1, 3, 5, 7, 9 — each row prints one more odd count of digits than the previous.

Why are there no spaces between digits?

print(j, end="") prints each digit immediately after the previous one on the same line — no space character is added.

Can I print only odd numbers instead of 1..i?

Yes. Change the inner loop to range(1, i + 1, 2) and print j to output 1, 13, 135, 1357, 13579 (see Example 3).

What is the difference between print with end= and print()?

print(j, end="") stays on the same line with no trailing space. print() ends the current line. Digits use end=""; the row break uses print() after the inner loop.

Why does it stop at 9?

Because the outer loop runs while i <= 9 (range(1, 10, 2)). Change 9 to any odd maximum to extend the pattern.

What if the user enters an even maximum?

Subtract 1 to make it odd (see Example 2) so the last row still has an odd length.

What is the time complexity?

O(n²) for maximum row length n because total prints are 1+3+5+...+n.

How should I read max_n safely?

Use a try/except ValueError around int(input()) or check the raw string with .isdigit() before converting so bad input does not crash the script.

What happens if max_n 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? 🔊

Each row length increases by 2 because the outer loop uses range(..., 2) (1, 3, 5, 7, 9). The inner loop prints 1..i with end="" — total prints grow as O(n²) for maximum row length n.

Continue to Program 23

Move on to the number & asterisk mirror pattern in the Python number-pattern series.

Program 23 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

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Python Number Pattern 21 — Jump Number Triangle Python Number Pattern 23 — Number & Asterisk Mirror

Increasing Odd-Length Number Rows in Python

What You’ll Learn

Shape Rule

Outer Loop

Inner Loop

print end= vs print()

Live Preview

O(n²)

Introduction

Why it matters?

Outer i += 2

Inner 1..i

No spaces

Series Foundation

📝 Problem & Approach

Inputs & Outputs

Minimal workflow

Approach comparison

⚡ Quick Reference

📋 Fixed Max vs User Input vs Odd-Only Digits

When This Pattern Shows Up

Post-jump 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_n = 9

How It Works

📈 User Input

Example 2 — User Input

How It Works

⚡ Odd-Only Digits

Example 3 — Odd-Only Digits range(..., 2)

How It Works

🧠 How the Algorithm Prints Rows

Set up

Outer loop + range step 2

Inner loop + print(j, end="")

New line

Odd-length rows complete

🔎 Worked Walkthrough — max_n = 9

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 input()

3. Keep print() Outside

4. Trace i and j on Paper

5. Dry-Run One Small n

Common Pitfalls

1. Newline Inside the Inner Loop

2. Forgetting range step 2

3. Adding Spaces Between Digits

4. Forgetting the Row Break

5. Unchecked input

Edge Cases

Single digit

Empty pattern

max_n < 0

Large width

Non-numeric input

User enters even

🎯 Practice Problems

1. Jump number triangle

2. Number & asterisk mirror

3. Spaced digits

4. No trailing space

Example 1 — Fixed `max_n = 9`

Example 3 — Odd-Only Digits `range(..., 2)`

🔎 Worked Walkthrough — `max_n = 9`

2. Validate `input()`

3. Keep `print()` Outside

`max_n < 0`