

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
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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



