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Collatz Conjecture

The Collatz conjecture, named after Lothar Collatz of Germany, proposed the conjecture in 1937. The conjecture states you must begin with any positive integer n: If it is an even number then halve it, or if it is an odd number then triple it and add 1. Do this recursively, and your result should always reach 1.

Please note: A maximum input length of 500 digits is enforced. Everything except positive numbers will be stripped out (including plus and minus signs) and must equal 2 or above (1 is not accepted). By entering ridiculously large numbers, the resulting page may be a few megabytes big.

Starting Integer: (required)
Information

Main article: Collatz Conjecture - Information

It has long been undecided if the first step should or should not include the starting integer. Many documents state this uncertainty on the Internet. I'm following the OEIS examples A006577 and A008884. On my page, I shall use step 0 to show the starting integer.

Other names for the Collatz conjecture include the 3n+1 conjecture, the Ulam conjecture, Kakutani's problem, the Thwaites conjecture, Hasse's algorithm, and the Syracuse problem.

This tool was inspired by xkcd's comic #710 "Collatz Conjecture" from 05/03/2010.


Statistics

I thought it might be interesting to some to include statistics about the data generated by use of this tool.

I have a total submission count of 1,884,457, and 1,676,246 of those submissions are unique. The greatest number of steps I've seen from a single submitted number so far is 62,118 (abiding by the 500 digit restriction) and was found on 18/01/2015. The most popular submitted number has been submitted 19,141 times. The second-most popular submitted number has been submitted 476 times. The total maximum amount of digits (all steps end-to-end) produced from a single submitted number is 15,813,021. The grand total number of steps produced by this tool is 703,664,532, or 566,781,665 for only unique submissions. This means a staggering grand total number of 66,495,011,254 digits were generated, or 41,624,329,374 digits if we count only unique submissions (these include step #0 and the final result of 1). Those big numbers equate to 61.93 GiBs and 38.77 GiBs of data respectively. The last submission (a unique number too!) happened this immediate second.

These statistics began recording back in July, 2012.

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