A273216 Initial prime numbers encountered by Collatz (3x+1) evaluation at odd, composite, ascending starts.

7, 23, 2, 19, 41, 19, 53, 59, 17, 37, 29, 83, 43, 137, 37, 13, 113, 29, 61, 2, 131, 137, 53, 137, 149, 79, 167, 173, 11, 179, 137, 139, 47, 97, 19, 229, 53, 137, 109, 83, 173, 233, 239, 137, 31, 127, 257, 263, 19, 233, 139, 281, 71, 293

Offset

1,1

Comments

The sequence is infinite provided the Collatz conjecture is true.

Conjecture: every prime number is encountered except 3.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The first eligible composite is 9.  The mechanism gives 3 * 9 + 1 = 28, followed by 28/2 = 14,then 14/2 = 7.  This is the first prime encountered starting at 9 and enters the sequence as a(1).
The next odd composite is 15.  The mechanism gives 3 * 15 + 1 = 46, followed by 46/2 = 23.  This is the first prime encountered starting at 15 and enters the sequence as a(2).

Mathematica

nwp[n_]:=NestWhile[If[EvenQ[#], #/2, 3#+1]&, n, !PrimeQ[#]&]; nwp/@Select[ Range[ 1, 251, 2], CompositeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 05 2020 *)

Prog

(PARI)
genit(maxx)={i5=9; while(i5<=maxx, evalx=i5; if(!isprime(evalx), while(!isprime(evalx), if(evalx%2==0, evalx=evalx/2, evalx=3*evalx+1)); print1(evalx, ", ")); i5+=2); }

Crossrefs

Cf. A014682 The Collatz or 3x+1 function.

Sequence in context: A197853 A087184 A067959 * A367002 A070411 A340631

Adjacent sequences: A273213 A273214 A273215 * A273217 A273218 A273219

Keyword

nonn

Author

Bill McEachen, May 17 2016

Status

approved