Sieve of Sundaram
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 ()
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):
Double each number and add one:
The equivalent in Step 2 above, of the Sieve of Eratosthenes starting the at the next prime squared, is starting at for next index
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.