cp's OEIS Frontend

A031140 Position of rightmost 0 in 2^n increases.

%I A031140 #28 Feb 16 2025 08:32:35
%S A031140 10,20,30,40,46,68,93,95,129,176,229,700,1757,1958,7931,57356,269518,
%T A031140 411658,675531,749254,4400728,18894561,33250486,58903708,297751737,
%U A031140 325226398,781717865,18504580518,27893737353,103233492954
%N A031140 Position of rightmost 0 in 2^n increases.
%C A031140 "Positions" are counted 0,1,2,3,... starting with the least significant digit.
%C A031140 I.e., look for increasing number of nonzero digits after the rightmost digit '0'. - _M. F. Hasler_, Jun 21 2018
%H A031140 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Zero.html">Zero.</a>
%e A031140 From _M. F. Hasler_, Jun 21 2018: (Start)
%e A031140 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 A031140 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 A031140 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)
%t A031140 best = 0;
%t A031140 Select[Range[10000],
%t A031140  If[(t = First@
%t A031140        First@StringPosition[StringReverse@ToString@(2^#), "0"]) >
%t A031140 best, best = t; True] &] (* _Robert Price_, Oct 11 2019 *)
%o A031140 (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 A031140 Cf. A031141, A031142, A031143.
%K A031140 nonn,base
%O A031140 1,1
%A A031140 _Matthew Cook_, _Dan Hoey_, _Eric W. Weisstein_, _David W. Wilson_
%E A031140 More terms from _Dan Hoey_.