Syracuse numbers (a.k.a Collatz conjecture)

This page is about Syracuse numbers, also called 3n+1 conjecture (or Collatz conjecture): let's start with any integer number N, and apply following simple rules : if N is even N=N/2, if not N=3N+1. It seems that N will always drop to 1...but is it true for *any* value of N???

With this page you can try to find a new record (or a N value proving this conjecture is false) by using any starting N as big as you want : enter a value, and click on the button "go for syracuse". You can also automatically search for records by choosing N and clicking on "search for max height" or "search for max length" buttons, good luck :)

Hint: «All numbers up to 2⁶⁹ (590.295.810.358.705.651.712) [21 digits] have been checked once for convergence.» [1]

Number:
digits.
show Result details - During loops : show intermediate result show N
Search for max height : delta:
Search for max length : delta:

Some high scores: N=104899295810901231 needs 2254 iterations (Eric Roosendaal), with no n < N having more iterations.
Thr first N with 2000 iterations : N=377060271667498687 N=67457283406188652 (more details on Eric Roosendaal's «Delay Records» page).

Read more here: Wikipedia , Eric Roosendaal , Eric Farin , Pour la science (Jean-Paul Delahaye) , ...

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