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

1, 2, 4, 8, 16, 21, 32, 42, 64, 84, 85, 128, 168, 170, 256, 336, 340, 341, 453, 512, 672, 680, 682, 906, 909, 1024, 1344, 1360, 1364, 1365, 1812, 1813, 1818, 2048, 2688, 2720, 2728, 2730, 3624, 3626, 3636, 4096, 5376, 5440, 5456, 5460, 5461, 7248, 7252, 7272

Offset: 1

Author

Reinhard Zumkeller, Oct 08 2011

Keywords

• nonn

Comments

Union of A000079 and A078440;

A055509(a(n)) = 0; A078350(a(n)) <= 1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Collatz Problem
• Wikipedia, Collatz conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370; subsequence of A065090.

Cf. A221475 (odd numbers in this sequence).

Programs

Haskell

a196871 n = a196871_list !! (n-1)
a196871_list = filter
   (all (== 0) . map a010051 . takeWhile (> 2) . iterate a006370) [1..]

Mathematica

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 *)