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
Keywords
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
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
Comments