Number Pattern Generator
Generate arithmetic, geometric, Fibonacci, prime, square, cube sequences. Custom formula support.
About this tool
A Number Pattern Generator is a tool that automatically creates sequences of numbers based on mathematical rules, helping you understand and visualize how patterns evolve. Whether you're exploring arithmetic progressions, geometric sequences, Fibonacci numbers, prime numbers, or perfect squares and cubes, this tool generates as many terms as you need instantly. It's invaluable for students learning mathematics, educators preparing lessons, programmers building algorithms, and anyone curious about how numbers relate to each other.
Using the tool is straightforward: select a sequence type from the dropdown menu, set your starting values or parameters, and choose how many terms to generate. For simple sequences like arithmetic or geometric progressions, you provide the first term and the common difference or ratio. For more advanced patterns like custom formulas, you can enter your own mathematical expression using standard notation, and the tool will compute each term according to your rules. The generator displays results in a clean, easy-to-read format, and you can copy or export the sequence for use in spreadsheets, code, or mathematical analysis.
This tool handles sequences from 1 to 1,000 terms, making it suitable for everything from classroom demonstrations to computational analysis. It's particularly helpful for identifying number properties, verifying mathematical hypotheses, and exploring the deeper patterns that connect arithmetic, geometry, and number theory. Whether you're a mathematician, student, or developer, the Number Pattern Generator transforms manual calculation into instant insight.
Frequently Asked Questions
Code Implementation
def arithmetic(a1, d, n):
"""Arithmetic sequence: a1, a1+d, a1+2d, ..."""
return [a1 + i * d for i in range(n)]
def geometric(a1, r, n):
"""Geometric sequence: a1, a1*r, a1*r^2, ..."""
return [a1 * (r ** i) for i in range(n)]
def fibonacci_like(a1, a2, n):
"""Fibonacci-like: starts with a1, a2; each term = sum of previous two."""
seq = [a1, a2]
for _ in range(n - 2):
seq.append(seq[-1] + seq[-2])
return seq[:n]
def primes(n):
"""First n prime numbers using trial division."""
result = []
candidate = 2
while len(result) < n:
if all(candidate % p != 0 for p in result if p * p <= candidate):
result.append(candidate)
candidate += 1
return result
# Examples
print("Arithmetic (a=3, d=4):", arithmetic(3, 4, 8))
# [3, 7, 11, 15, 19, 23, 27, 31]
print("Geometric (a=2, r=3):", geometric(2, 3, 6))
# [2, 6, 18, 54, 162, 486]
print("Fibonacci-like (1,1):", fibonacci_like(1, 1, 8))
# [1, 1, 2, 3, 5, 8, 13, 21]
print("First 8 primes:", primes(8))
# [2, 3, 5, 7, 11, 13, 17, 19]
print("Squares:", [i**2 for i in range(1, 9)])
# [1, 4, 9, 16, 25, 36, 49, 64]Comments & Feedback
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