login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A216189 Numbers n whose odd Collatz steps (except for 1) are all primes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)