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A276290
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Products of odd primes p and q such that either p or q is in the trajectory of (p*q)+1 under the Collatz 3x+1 map (A014682).
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2
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25, 35, 55, 65, 77, 85, 95, 115, 133, 143, 145, 155, 161, 185, 203, 205, 209, 215, 217, 235, 253, 259, 265, 287, 295, 305, 329, 341, 355, 365, 371, 391, 395, 403, 407, 415, 427, 437, 445
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OFFSET
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1,1
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COMMENTS
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Conjecture: If n is the product of two odd primes p and q and p is equal to 3, then neither p nor q is in the trajectory of (p*q)+1 under the Collatz 3x+1 map (A014682). - Marina Ibrishimova, Aug 29 2016
If there were any multiples of three present in this sequence, then there would also be nontrivial cycles among Collatz-trajectories. It has been empirically checked that for the first 2^22 = 4194304 primes from p=2 to p=71378569, 3*p certainly is not included in this sequence. - Antti Karttunen, Aug 30 2016
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LINKS
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MATHEMATICA
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Select[Range[9, 450, 2], And[PrimeOmega@ # == 2, Function[w, Total@ Boole@ Map[MemberQ[NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, Times @@ w + 1, # > 1 &], #] &, w] > 0]@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ #, {1}]] &] (* Michael De Vlieger, Aug 28 2016 *)
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PROG
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(JavaScript) function isitCollatzProduct(p, q){var n=p*q; var cur=n+1; while(cur!=p&&cur!=q&&cur!=2){if(cur%2!=0){cur=3*cur+1}else{cur=cur/2}}if(cur==p||cur==q){return cur}else{return 0}}
(PARI) has(p, q)=my(t=p*q+1); while(t>2, t=if(t%2, 3*t+1, t/2); if(t==p || t==q, return(1))); 0
list(lim)=forprime(p=3, lim\3, forprime(q=3, min(lim\p, p), if(has(p, q), listput(v, p*q)))); Set(v) \\ Charles R Greathouse IV, Aug 27 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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