Bulk Richardson Number Calculator

This calculator can be used to check if a number is a Richardson number, which is a number that can be expressed as the sum of two or more consecutive positive integers in exactly two different ways.

Input Parameters

Calculation Results

Calculation Formula

A number n is a Richardson number if it can be expressed as the sum of consecutive integers in exactly two different ways:

n = a + (a+1) + (a+2) + ... + (b)
n = c + (c+1) + (c+2) + ... + (d)

Where:
a, b, c, d are positive integers and a ≠ c

Bulk Richardson Number Calculator Calculator Usage Guide

Learn how to use the Bulk Richardson Number Calculator calculator and its working principles

What is a Richardson Number?

A Richardson number is a number that can be expressed as the sum of two or more consecutive positive integers in exactly two different ways. For example, 30 is a Richardson number because:

  • 30 = 7 + 8 + 9 + 6
  • 30 = 12 + 13 + 5

How to use this calculator

  1. Enter a positive integer in the "Number to check" field.
  2. Click the "Calculate" button.
  3. The calculator will determine if the number is a Richardson number and show the representations if it is.

Working Principle

The calculator works by finding all possible consecutive sequences of integers that sum up to the input number. It does this by:

  1. Starting with the smallest possible sequence length (1).
  2. Incrementing the sequence length until the sum exceeds the target number.
  3. For each sequence, calculating the starting and ending terms.
  4. Checking if the sequence sums to the target number.
  5. Tracking if there are exactly two different sequences that meet this condition.

Example

If you enter 30, the calculator will find that:

  • 7 + 8 + 9 + 6 = 30
  • 12 + 13 + 5 = 30

Since there are exactly two representations, 30 is confirmed as a Richardson number.