A254783 Numbers n such that A033493(n)/n is an integer.

1, 57, 847, 1694, 3039, 3388, 3479, 6078, 6776, 6958, 13916, 27832, 55664, 111328, 236107, 246721, 311257, 493442, 622514, 986884, 1245028, 1328233, 1973768, 2052521, 2490056, 2656466, 3947536, 4105042, 4980112, 8210084

Offset: 1

Author

Derek Orr, Feb 07 2015

Keywords

• nonn
• more
• hard

Comments

If A033493(n)/n = M is even, then 2*n is a member of the sequence and A033493(2*n)/(2*n) = M/2 + 1.

a(31) > 10^7. - Derek Orr, Mar 12 2015

Sum of reciprocals seems to converge quickly to 1.0208... - Derek Orr, Mar 12 2015

Links

• Eric Weisstein's World of Mathematics, CollatzProblem
• Wikipedia, Collatz conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A033493.

Programs

Mathematica

a033493[n_] := Block[{f}, f[1] = 1; f[x_Integer?OddQ] := 3 x + 1; f[x_Integer?EvenQ] := x/2; -1 + Plus @@ FixedPointList[f, n]]; Select[Range[10^5], IntegerQ[a033493[#]/#] &] (* Michael De Vlieger, Feb 09 2015, after Alonso del Arte at A033493 *)

PARI

Tsum(n)=s=n;while(n!=1,if(n==Mod(0,2),n=n/2;s+=n);if(n==Mod(1,2)&&n!=1,n=3*n+1;s+=n));s
for(n=1,10^6,if(type(Tsum(n)/n)=="t_INT",print1(n,", ")))