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).

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

Offset: 1

Author

Marina Ibrishimova, Aug 27 2016

Keywords

• nonn

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 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

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

Crossrefs

Cf. A014682, A065091, A276260.

Subsequence of A046315.

Programs

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}}

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 *)

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

Extensions

Terms corrected by Charles R Greathouse IV, Aug 27 2016