

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to 3x+1 (or Collatz) problem


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

Cf. A014682, A065091, A276260.
Subsequence of A046315.
Sequence in context: A193165 A060976 A036320 * A173251 A063149 A046423
Adjacent sequences: A276287 A276288 A276289 * A276291 A276292 A276293


KEYWORD

nonn


AUTHOR

Marina Ibrishimova, Aug 27 2016


EXTENSIONS

Terms corrected by Charles R Greathouse IV, Aug 27 2016


STATUS

approved



