A225038 Numbers n such that at least one member of Collatz (3x+1) trajectory of n is >= n^2.

1, 3, 7, 27, 31, 41, 47, 54, 55, 62, 63, 71, 73, 82, 83, 91, 94, 95, 6631675, 7460635, 319804831, 379027947, 426406441, 479707247, 568541921, 598957743, 639609662, 639609663, 719560871, 758055894, 758055895, 852812882, 852812883, 898436615, 959414494, 959414495, 1010741193, 1079341307, 1137083842, 1137083843, 1410123943

Offset: 1

Author

Jayanta Basu, Apr 25 2013

Keywords

• nonn

Comments

Many of these numbers are on the same trajectory. For instance, the numbers from 27 to 95 are all on the Collatz trajectories of 27 and 54. See Roosendaal's web page for more possibilities. - T. D. Noe, Apr 25 2013

Examples

			3 is a member since both 16 and 10 both belong to Collatz trajectory of 3 that are >= 3^2 = 9.
		

Links

• Eric Roosendaal, 3x+1 path records

Crossrefs

Cf. A025586, A070165.

Programs

Mathematica

Coll[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Max[Coll[n]] >= n*n, AppendTo[t, n]], {n, 1000}]; t

Formula

Numbers n such that A025586(n) >= n^2.

Extensions

Extended by T. D. Noe, Apr 25 2013