OFFSET
1,2
COMMENTS
Böhm and Sontacchi show a(n) needs the 3x+1 operator at most twice to reach 1 in the Collatz 3x+1 problem.
Conjecture: Odd part of a(n) is of form [(1/6)*(8^m-(-1)^m-3)*4^k-1]/3, k,m>0.
REFERENCES
C. Böhm and G. Sontacchi: On the Existence of Cycles of given Length in Integer Sequences like x_(n+1) = x_n/2 if x_n even, and x_(n+1) = 3x_n + 1 otherwise. Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie VIII 64 (1978), 260-264.
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Nov 24 2010
STATUS
approved