A216189 Numbers n whose odd Collatz steps (except for 1) are all primes.

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 19, 20, 21, 22, 24, 25, 26, 28, 29, 34, 35, 37, 38, 39, 40, 44, 45, 48, 49, 52, 53, 56, 58, 59, 67, 68, 69, 74, 76, 77, 80, 85, 87, 88, 89, 96, 99, 101, 104, 106, 112, 116, 117, 118, 119, 131, 134, 136, 141, 148, 149

Offset

1,1

Comments

Powers of 2 are not included as they don't have odd Collatz steps. The number n itself (if odd) is not counted as an odd step. [Corrected by Jianing Song, Dec 09 2018]

Links

Table of n, a(n) for n=1..62.

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

Example

7 is in this sequence because 7*3+1 = 22; 22/2 = [11]; 11*3+1 = 34; 34/2 = [17]; 17*3+1 = 52; 52/2 = 26; 26/2 = [13]; 13*3+1 = 40; 40/2 = 20; 20/2 = 10; 10/2 = [5]; 5*3+1 = 16; 16/2 = 8; 8/2 = 4; 4/2 = 2; 2/2 = 1. 11, 17, 13 and 5 are all primes.
15 is not in this sequence because 15*3+1 = 46; 46/2 = [23]; 23*3+1 = 70; 70/2 = 35, which isn't a prime number.

Mathematica

Select[Range[3, 150], And[AllTrue[Select[Rest@ #2, OddQ], PrimeQ], !IntegerQ@ Log2@ #1] & @@ {#, NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, # > 2 &, 1, Infinity, -1]} &] (* Michael De Vlieger, Nov 07 2018 *)

Crossrefs

Cf. A006577, A177000.

Sequence in context: A052294 A336101 A267895 * A191916 A254614 A320698

Adjacent sequences: A216186 A216187 A216188 * A216190 A216191 A216192

Keyword

nonn

Author

Alessandro Polcini, Oct 10 2018

Status

approved