%N Position of rightmost 0 in 2^n increases.
%C "Positions" are counted 0,1,2,3,... starting with the least significant digit.
%C I.e., look for increasing number of nonzero digits after the rightmost digit '0'. - _M. F. Hasler_, Jun 21 2018
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Zero.html">Zero.</a>
%e From _M. F. Hasler_, Jun 21 2018: (Start)
%e 2^10 = 1024 is the first power of 2 to have a digit '0', which is the third digit from the right, i.e., it has to its right no digit '0' and two nonzero digits.
%e 2^20 = 1048576 is the next larger power with a digit '0' having to its right no digit '0' and more (namely 5) nonzero digits than the above 1024.
%e After 2^46 = 70368744177664 there is 2^52 = 4503599627370496 having a '0' further to the left, but this digit has another '0' to its right and therefore cannot be considered: The next term having more nonzero digits after its rightmost '0' is only 2^68. (End)
%o (PARI) m=0;for(k=0,oo,d=digits(2^k);for(j=0,#d-1,d[#d-j]||(j>m&&(m=j)&&print1(k",")||break))) \\ _M. F. Hasler_, Jun 21 2018
%Y Cf. A031141, A031142, A031143.
%A _Matthew Cook_, _Dan Hoey_, _Eric W. Weisstein_, _David W. Wilson_
%E More terms from _Dan Hoey_.