Sieve of Sundaram

Description

The Sieve of Sundaram is a sieve for a range of odd prime numbers.The sieve starts out listing the natural numbers to like the following example ()

Step 2

Then it finds all numbers of form ( fancy way of saying start at and increase by , for each not already eliminated ) and eliminates them (empty cells):

Step 3

Double each number and add one:

Optimization

1. The equivalent in Step 2 above, of the Sieve of Eratosthenes starting the at the next prime squared, is starting at for next index

Generalization

Looking close, if you know modular arithmetic, you'll note the remainder 1 forms the modular multiplicative group modulo 2. This generalizes to the modular multiplicative group mod any natural number.