%I #10 Sep 25 2014 21:46:00

%S 5461,7281,29125,38833,51777,77667,103555,116501,122731,138073,155333,

%T 163641,184097,207109,245463,276145,276147,310669,327283,368193,

%U 368195,414221,414225,436377,466005,490925,552291,552293,581835,621333,654565,689583,736387,736389,828437,828451

%N Odd numbers n containing 16384 as the highest power of 2 in the Collatz (3x+1) iteration.

%C a(n)*2^k also contains 16384 as the highest power of 2 for any k >= 0.

%o (PARI)

%o Max2(n)=v=[n]; while(n!=1, if(n==Mod(0, 2), n=n/2; v=concat(v, n)); if(n==Mod(1, 2)&&n!=1, n=3*n+1; v=concat(v, n))); k=1; while(vecsearch(vecsort(v), 2^k), k++); 2^(k-1)

%o n=1; while(n<10^4, if(n%2&&Max2(n)==16384, print1(n, ", ")); n++)

%Y Cf. A008908, A010120.

%K nonn

%O 1,1

%A _Derek Orr_, Sep 22 2014