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

1,2

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

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, CollatzProblem

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 (or Collatz) problem

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 *)

Prog

(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, ", ")))

Crossrefs

Cf. A033493.

Sequence in context: A098995 A210156 A210149 * A233370 A008390 A231311

Adjacent sequences: A254780 A254781 A254782 * A254784 A254785 A254786

Keyword

nonn,more,hard

Author

Derek Orr, Feb 07 2015

Status

approved