A031140 Position of rightmost 0 in 2^n increases.

10, 20, 30, 40, 46, 68, 93, 95, 129, 176, 229, 700, 1757, 1958, 7931, 57356, 269518, 411658, 675531, 749254, 4400728, 18894561, 33250486, 58903708, 297751737, 325226398, 781717865, 18504580518, 27893737353, 103233492954

Offset: 1

Author

Matthew Cook, Dan Hoey, Eric W. Weisstein, David W. Wilson

Keywords

• nonn
• base

Comments

"Positions" are counted 0,1,2,3,... starting with the least significant digit.

I.e., look for increasing number of nonzero digits after the rightmost digit '0'. - M. F. Hasler, Jun 21 2018

Examples

			From _M. F. Hasler_, Jun 21 2018: (Start)
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.
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.
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)
		

Links

• Eric Weisstein's World of Mathematics, Zero.

Crossrefs

Cf. A031141, A031142, A031143.

Programs

Mathematica

best = 0;
Select[Range[10000],
 If[(t = First@
       First@StringPosition[StringReverse@ToString@(2^#), "0"]) >
best, best = t; True] &] (* Robert Price, Oct 11 2019 *)

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

Extensions

More terms from Dan Hoey.