Check Pronic Number in Python

What You’ll Learn

A pronic number (also called oblong or rectangular) equals k * (k + 1) for some integer k >= 0. Examples: 0, 2, 6, 12, 20. Non-examples: 1, 9, 15. This tutorial covers an integer loop check, a live finder for k, worked Python examples, edge cases, and complexity.

📝 Problem & Approach

Given an integer n, decide whether it equals k*(k+1) for some k >= 0.

# 12 -> 3*4 = 12   pronic
# 9  -> 3*3 = 9    not consecutive
# 0  -> 0*1 = 0    pronic
# 2  -> 1*2 = 2    pronic

Inputs & Outputs

Minimal workflow

function isPronic(n):
    if n < 0:
        return false
    k = 0
    while true:
        p = k * (k + 1)
        if p == n:
            return true
        if p > n:
            return false
        k = k + 1

Method comparison

🔮 Live Preview

Grows k from 0 and reports the matching pair when n is pronic.

Press “Run check”.

Examples Gallery

Three complete Python programs — check 12, list pronic values from 1 to 20, and generate the sequence by multiplying consecutive integers. Click View Output to reveal sample console results.

def is_pronic(n: int) -> bool:
    if n < 0:
        return False

    k = 0
    while True:
        product = k * (k + 1)
        if product == n:
            return True
        if product > n:
            return False
        k += 1


number = 12
if is_pronic(number):
    print(f"{number} is a pronic number.")
else:
    print(f"{number} is not a pronic number.")

12 is a pronic number.

def is_pronic(n: int) -> bool:
    if n < 0:
        return False
    k = 0
    while True:
        product = k * (k + 1)
        if product == n:
            return True
        if product > n:
            return False
        k += 1


print("Pronic numbers in the range 1 to 20:")
for value in range(1, 21):
    if is_pronic(value):
        print(value, end=" ")
print()

Pronic numbers in the range 1 to 20:
2 6 12 20

print("Pronic numbers for k = 0 to 6:")
for k in range(0, 7):
    value = k * (k + 1)
    print(f"{k} * {k + 1} = {value}")

Pronic numbers for k = 0 to 6:
0 * 1 = 0
1 * 2 = 2
2 * 3 = 6
3 * 4 = 12
4 * 5 = 20
5 * 6 = 30
6 * 7 = 42

🔎 Worked Walkthrough — 12 vs 9

Compare the grow-k loop on a yes case and a no case.

12 hits exactly at k = 3; 9 is skipped between 6 and 12.

⚖️ Facts Worth Knowing

Handy follow-ups interviewers sometimes ask.

🎯 Practice Problems

Try these variations to lock in the pattern.

Notes

⏱️ Time and Space Complexity

Since k*(k+1) grows like k², the search stops after about sqrt(n) steps.

💡 Best Practices