The first prime that produces exactly n odd primes in the Collatz iteration; the other terms are 1 or even.
2, 5, 3, 17, 11, 7, 19, 101, 67, 89, 59, 157, 13397, 2312267, 97760291, 1042776437, 711868714549, 3796633144261, 20734679145190741, 7077437148225106261, 648477036610609831222431913301, 7787949174500975808778564850143642861006312789
0
Note that the plot uses two logarithms; this sequence grows very rapidly.
T. D. Noe, Plot of 29 terms
T. D. Noe, Table of 29 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 &]; t2 = Table[Length[Select[Collatz[n], OddQ]] - 1, {n, c}]; Table[c[[Position[t2, n, 1, 1][[1, 1]]]], {n, 0, Max[t2]}]
nonn,nice
T. D. Noe, Dec 28 2014