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%I #14 Apr 25 2013 16:19:35
%S 1,3,7,27,31,41,47,54,55,62,63,71,73,82,83,91,94,95,6631675,7460635,
%T 319804831,379027947,426406441,479707247,568541921,598957743,
%U 639609662,639609663,719560871,758055894,758055895,852812882,852812883,898436615,959414494,959414495,1010741193,1079341307,1137083842,1137083843,1410123943
%N Numbers n such that at least one member of Collatz (3x+1) trajectory of n is >= n^2.
%C 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
%H Eric Roosendaal, <a href="http://www.ericr.nl/wondrous/pathrecs.html">3x+1 path records</a>
%F Numbers n such that A025586(n) >= n^2.
%e 3 is a member since both 16 and 10 both belong to Collatz trajectory of 3 that are >= 3^2 = 9.
%t Coll[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; Do[If[Max[Coll[n]] >= n*n, AppendTo[t, n]], {n, 1000}]; t
%Y Cf. A025586, A070165.
%K nonn
%O 1,2
%A _Jayanta Basu_, Apr 25 2013
%E Extended by _T. D. Noe_, Apr 25 2013