

A276290


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).


2



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

1,1


COMMENTS

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 Collatztrajectories. 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


LINKS



MATHEMATICA

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 *)


PROG

(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==pcur==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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



