O problema de Collatz
Autor: Ricardo Aldabó Lopez | Publicado: 2015-10-27T06:18:00-07:00

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É um
enigma famoso que intriga os maiores matemáticos do mundo. Eles acreditam
conhecer a resposta, mas ninguém consegue prová-la. 







Pense
um número. Agora aplique as seguintes regras repetidamente:



· Se o número for
par, divida-o por 2.



· Se o número for
ímpar, multiplique-o por 3 e some 1.







O
que acontece? 







Como
exemplo, o número 11 é ímpar e o próximo número será 3 x 11 + 1 = 34. Este
número é par, portanto devemos dividi-lo por 2 para obter 17. Este é ímpar, e a
próxima operação resulta em 52. Depois disto, os números que se seguem são 26,
13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
 A partir daqui, chegamos a 4, 2, 1, 4, 2, 1
indefinidamente. 







Por
isso geralmente acrescentamos uma terceira regra: quando chegar a 1, pare.







Em
1937, Lothar Collatz se perguntou se esse procedimento sempre levaria ao número
1, independentemente do número em que começássemos. Mais de 70 anos depois,
ainda não sabemos a resposta. A maioria dos matemáticos acredita que a
conjectura seja verdadeira.