The 3n+1 sequence has probably consumed more CPU time than any other number theoretic conjecture. The reason being that its statement is so simple, that most amateurs will feel compelled to write programs to test it. This sequence, attributed to Lothar Collatz, has bee given various names, including Ulam's conjecture, Syracuse problem, Kakutani's problem and Hasse's algorithm. The conjecture is based on the iteration defined by: n[i+1] = if n[i] is even then n[i]/2 else 3*n[i]+1 .