A note on the "3x + 1 ' problem - H. Wilf, March 19, 1993. Take a positive integer n and repeat the following operations: if n is odd then replace n ...

3x +1 problem , sequences related to (start): 3x +1 problem , (01): A000546 , A001281 , A005186 , A006370 ... 3x +1 problem , (02): A006885 , A008873 , A008874 , A008875 , A008876 , ...

The 3x + 1 problem is a notorious problem of elementary number theory. ... Main Theorem 1 There are no non-trivial 2-cycles for the 3x + 1 problem . ...

It would be better to say that 3x + 1 has only one positive loop. ... Sequences in the Collatz 3x +1 problem . moved: It has been shown that a binary tree can be ...

... let f(x) = 3x +1 . The 3x +1 problem conjectures that for each ... f applied to x yields 1 . Recently, Charles C. Cadogan has claimed the first positive solution to this problem . ...

This paper presents a solution to the 3x + 1 problem . The method employs the convergence of the trajec ... the 3x + 1 problem since two trajectories, having coalesced, can ...

The 3x +1 conjecture states that iteration of that function on positive ... The 3x +1 problem concerns questions about the iteration of a deceptively simple function ...

The 3x + 1 problem is de?ned by a sequence of natural numbers, generated ... 2. The approach can be applied to the 3x 1 problem , de?ned by T (x) ...

1996), ... Paul Andaloro: The 3x +1 problem and directed graphs. ... Monthly 92 (1985), 3-23. 1973 Jeffrey Lagarias: The set of rational cycles for the 3x +1 problem . Acta Arithm. ...

Problem : (x + 1 ) (x2 - 3x + 2) Analyze: Problem : x(x ? 1 )(2x + 1 ) ... Problem : (x2-3x +1 )-(x2+2x+7) Analyze: (x2-3x +1 )-(x2+2x+7) Problem : Area of x (x+6) ...