Number of primes in Collatz sequences having only 1, even numbers, and primes.
1, 3, 2, 6, 5, 3, 4, 7, 6, 7, 3, 11, 9, 10, 8, 9, 7, 12, 10, 5, 8, 6, 9, 4, 10, 8, 5, 3, 4, 7, 10, 8, 11, 6, 9, 7, 12, 5, 3, 11, 4, 10, 11, 12, 13, 4, 7, 6, 12, 5, 11, 6, 4, 7, 8, 10, 8, 3, 8, 6, 9, 7, 5, 8, 6, 9, 4, 7, 10, 11, 6, 9, 4, 8, 9, 9, 14, 12, 12, 10, 13
1
This sequence is one more than S000440 because we count 2 with the primes.
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]], {n, Take[c, 1000]}]
nonn
T. D. Noe, Jan 06 2015