Increasing Jump Number Triangle Pattern in PHP

What You’ll Learn

The increasing jump number triangle starts each row at i and jumps forward with a decreasing step m — a natural step after the continuous counter in Program 20. This tutorial covers the shape rule, step logic, a live preview, algorithm steps, worked PHP examples, edge cases, and complexity.

📝 Problem & Approach

Given a positive integer rows, print an increasing jump number triangle: row i starts with i, then prints i - 1 more values computed by adding a decreasing step m.

// rows = 5 (conceptual shape)
// 1
// 2 6
// 3 7 10
// 4 8 11 13
// 5 9 12 14 15

Inputs & Outputs

Minimal workflow

for i from 1 to rows:
    print i
    m = rows - 1
    k = i + m
    for j from 1 to i - 1:
        print k
        m = m - 1
        k = k + m
    print newline

Approach comparison

🔮 Live Preview

Choose a row count between 1 and 15 and draw the jump number triangle in the browser.

Press "Draw pattern".

Examples Gallery

Three complete PHP programs — fixed row count, user input, and custom initial step for m. Click View Output to reveal sample console results.

<?php
for ($i = 1; $i <= 5; $i++) {
    echo $i . " ";

    $m = 4;
    $k = $i + $m;

    for ($j = 1; $j < $i; $j++) {
        echo $k . " ";
        $m--;
        $k = $k + $m;
    }

    echo PHP_EOL;
}

1 
2 6 
3 7 10 
4 8 11 13 
5 9 12 14 15

<?php
echo "Enter the number of rows: ";
$rows = (int) trim(fgets(STDIN));

for ($i = 1; $i <= $rows; $i++) {
    echo $i . " ";

    $m = $rows - 1;
    $k = $i + $m;

    for ($j = 1; $j < $i; $j++) {
        echo $k . " ";
        $m--;
        $k = $k + $m;
    }

    echo PHP_EOL;
}

Enter the number of rows: 4
1 
2 5 
3 6 8 
4 7 9 10

<?php
$rows = 4;

for ($i = 1; $i <= $rows; $i++) {
    echo $i . " ";

    $m = 3;
    $k = $i + $m;

    for ($j = 1; $j < $i; $j++) {
        echo $k . " ";
        $m--;
        $k = $k + $m;
    }

    echo PHP_EOL;
}

1 
2 5 
3 6 8 
4 7 9 10

🔎 Worked Walkthrough — rows = 5

Trace each outer-loop value of i, the initial m, and the numbers printed on each row.

Total number prints: 1 + 2 + 3 + 4 + 5 = 15 = 5×6/2.

🎯 Practice Problems

Try these variations to lock in the pattern.

Notes

⏱️ Time and Space Complexity

💡 Best Practices