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collatz-sieve

This repository contains convergence sieves for the verification of the Collatz problem.

To understand the *.map files, see the detailed description on the Wikipedia page.

For example, the 16 least-significant bits of a number n can be used as bit-index into the esieve-16.map. This result is that only 1720 out of 65536 numbers (about 2.6 %) must be checked for convergence.

I have found that these convergence sieves (considering values stored in bits) have a kind of internal structure. Specifically, sieves are formed by only several constantly repeated 64-bit patterns, so I store only indices into a small look-up table.

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