A221475 -id:A221475 - cp's OEIS frontend

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

Reinhard Zumkeller, Oct 08 2011

nonn

Union of A000079 and A078440;

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

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

Cf. A006370; subsequence of A065090.

Cf. A221475 (odd numbers in this sequence).

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

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 *)

A221476 Prime numbers having no additional odd primes in their Collatz (3x+1) trajectory.

Original entry on oeis.org

2, 5, 113, 227, 2417, 3637, 7253, 14549, 14563, 30559, 38677, 38833, 155333, 206923, 207121, 217309, 464213, 466033, 620771, 827693, 915737, 1100149, 1100353, 1220983, 1303873, 1472893, 1656901, 1963813, 2327483, 2475797, 2933717, 2933731, 3313777, 3491083

Offset: 1

T. D. Noe, Feb 14 2013

nonn

Sequence A221475 contains odd composite numbers with this property.

Index entries for sequences related to 3x+1 (or Collatz) problem

Cf. A221475.

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; n = 0; While[Length[t] < 50, n++; p = Prime[n]; If[Union[Drop[PrimeQ[Rest[Collatz[p]]], -2]] == {False}, AppendTo[t, p]]]; t

cp's OEIS Frontend

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

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