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A273216
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Initial prime numbers encountered by Collatz (3x+1) evaluation at odd, composite, ascending starts.
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1
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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
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1,1
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COMMENTS
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The sequence is infinite provided the Collatz conjecture is true.
Conjecture: every prime number is encountered except 3.
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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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 *)
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PROG
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(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); }
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CROSSREFS
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Cf. A014682 The Collatz or 3x+1 function.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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