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A273216 Initial prime numbers encountered by Collatz (3x+1) evaluation at odd, composite, ascending starts. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A070411 A340631 A167224

Adjacent sequences:  A273213 A273214 A273215 * A273217 A273218 A273219

KEYWORD

nonn

AUTHOR

Bill McEachen, May 17 2016

STATUS

approved

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)