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This package computes the iterates of the Collatz map: x -> x/2, if x is even; x -> (3x +1 )/2, if x is odd, until an iterate reaches one of the four known cycles (the ...

Abstract: The 3x + 1 problem concerns iteration of the map on the integers given ... The 3x +1 Conjecture asserts that for every positive integer n > 1 the forward ...

3x + 1 Problem . f:=proc(x) if x mod 2 =0 then x/2 else 3*x+1 fi; end; Working under Maple without the spreadsheet ...

Report:An experimental veri?cation of the 3x + 1 problem (3) ????,????,?????,??? ... 3x ± 1 ???????(1 )(Report:An experimental veri?cation of the 3x + 1 problem ...

This is known as the #3X +1 problem , the Collatz Conjecture, or a host of other names. Various cash prizes have been offered for its solution. ...

1 ,1 . The 3x +1 or Collatz problem is as follows: start with any number n. If n is even, divide it by 2, otherwise multiply it by 3 and add 1 . Do we always reach 1 ? ...

The problem dates from before World War II, when it seems to have been proposed ... look at the operation X 3X + 1 , we may neglect the addition of one, ...

the 3x + 1 problem , we proceed to another representation of sequences. ... Corollary 1 . The 3x + 1 conjecture is true if and only if for every ...