OFFSET
0,6
COMMENTS
For transient lengths for iterations of A062401(x) or A062402(x) if started at 2^n, A096994(n) + 1 = A096995(n). Corresponding cycle lengths satisfy A096852(n-1) = A096857(n). Behind these observations several relationships stand, e.g., sigma(A062401(x)) = A062402(sigma(x)) or phi(A062402(x)) = A062401(phi(x)).
EXAMPLE
n=0: trajectory = {1,1,..} so a(0)=0;
n=14: transient-length=14, cycle-length=2, a(14)=14, A096852(14)=2; trajectory ={16384, 27000, 23040, 21600, 17280, 15360, 15488, 13824, 9600, 7680, 7200, 12960, 11880, 11520, [10368,14080], 10368, ...}.
Values of a(n) for n > 31, with -1 signifying transient lengths yet unknown after 10^4 iterations of f(x): -1, 7, 51, 70, 23, 39, 11, -1, 37, 107, 30, -1, 145, 25, 21, 36, -1, -1, -1, -1, 31, -1, 452, -1, 449, 447, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 40, -1, -1, -1, -1, -1, -1, -1, 279, -1. - Michael De Vlieger, May 15 2017
MATHEMATICA
With[{nn = 10^3}, Table[Count[Values@ PositionIndex@ #, k_ /; Length@ k == 1] &@ NestList[EulerPhi@ DivisorSigma[1, #] &, 2^n, nn] /. k_ /; k == nn + 1 -> -1, {n, 31}] ] (* Michael De Vlieger, May 15 2017, Version 10 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Labos Elemer, Jul 22 2004
STATUS
approved