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A031140
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Position of rightmost 0 in 2^n increases.
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5
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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
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OFFSET
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1,1
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COMMENTS
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"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
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LINKS
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Eric Weisstein's World of Mathematics, Zero.
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EXAMPLE
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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)
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MATHEMATICA
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best = 0;
Select[Range[10000],
If[(t = First@
First@StringPosition[StringReverse@ToString@(2^#), "0"]) >
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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