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%I #7 Sep 25 2014 21:46:11
%S 14563,17259,19417,20455,21845,25889,27273,30683,34519,38835,40911,
%T 46025,51779,54547,58253,61367,64647,69037,72729,77669,81821,92049,
%U 92051,96971,103557,107623,109093,109095,122733,129295,138077,143497,145457,145459,153243,155341,161435
%N Odd numbers n containing 65536 as the highest power of 2 in their Collatz (3x+1) iteration.
%C a(n)*2^k also contains 65536 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)==65536, print1(n, ", ")); n++)
%Y Cf. A008908, A010120.
%K nonn
%O 1,1
%A _Derek Orr_, Sep 22 2014