Number of odd primes in Collatz sequences having only 1, even numbers, and primes.
0, 2, 1, 5, 4, 2, 3, 6, 5, 6, 2, 10, 8, 9, 7, 8, 6, 11, 9, 4, 7, 5, 8, 3, 9, 7, 4, 2, 3, 6, 9, 7, 10, 5, 8, 6, 11, 4, 2, 10, 3, 9, 10, 11, 12, 3, 6, 5, 11, 4, 10, 5, 3, 6, 7, 9, 7, 2, 7, 5, 8, 6, 4, 7, 5, 8, 3, 6, 9, 10, 5, 8, 3, 7, 8, 8, 13, 11, 11, 9, 12, 2, 10
1
Sequence A177000 has the prime numbers that begin these Collatz sequences.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, MathWorld: Collatz Problem
Wikipedia, Collatz conjecture
(Mma) (* the table c contains terms from A177000 *) Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[Length[Select[Collatz[n], OddQ]] - 1, {n, Take[c, 1000]}]
nonn
T. D. Noe, Dec 28 2014