Prime numbers whose Collatz sequence contains only 3 primes.
3, 13, 53, 853, 3413, 218453, 3495253, 13981013, 3665038759253, 61489146912365172053, 4029752732048763915687253, 24702312370627455023695143468520087008697596728669986995084284588354800989853013
1
These are the terms in A177000 that end in the digit 3. Note that the plot uses two logarithms; this sequence grows very rapidly. These are numbers of the form (5*2^n-1)/3, where n is in S000445.
T. D. Noe, Plot of 15 terms
T. D. Noe, Table of 15 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 &]; ps = Flatten[Position[c, _?(Mod[#, 10] == 3 &)]]; c[[ps]]
Cf. A177000, S000442, S000445.
nonn
T. D. Noe, Jan 06 2015