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A196871 Numbers having no odd primes in their Collatz (3x+1) trajectory.

%I A196871 #17 Feb 16 2025 08:33:15
%S A196871 1,2,4,8,16,21,32,42,64,84,85,128,168,170,256,336,340,341,453,512,672,
%T A196871 680,682,906,909,1024,1344,1360,1364,1365,1812,1813,1818,2048,2688,
%U A196871 2720,2728,2730,3624,3626,3636,4096,5376,5440,5456,5460,5461,7248,7252,7272
%N A196871 Numbers having no odd primes in their Collatz (3x+1) trajectory.
%C A196871 Union of A000079 and A078440;
%C A196871 A055509(a(n)) = 0; A078350(a(n)) <= 1.
%H A196871 Reinhard Zumkeller, <a href="/A196871/b196871.txt">Table of n, a(n) for n = 1..1000</a>
%H A196871 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CollatzProblem.html">Collatz Problem</a>
%H A196871 Wikipedia, <a href="http://en.wikipedia.org/wiki/Collatz_conjecture">Collatz conjecture</a>
%H A196871 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%t A196871 Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Join[{1, 2}, Select[Range[3, 10000], Union[Drop[PrimeQ[Collatz[#]], -2]] == {False} &]] (* _T. D. Noe_, Jan 22 2013 *)
%o A196871 (Haskell)
%o A196871 a196871 n = a196871_list !! (n-1)
%o A196871 a196871_list = filter
%o A196871    (all (== 0) . map a010051 . takeWhile (> 2) . iterate a006370) [1..]
%Y A196871 Cf. A006370; subsequence of A065090.
%Y A196871 Cf. A221475 (odd numbers in this sequence).
%K A196871 nonn
%O A196871 1,2
%A A196871 _Reinhard Zumkeller_, Oct 08 2011