Deleting every other number on a circle

MediumCombinatorics Brainteasers~8m

The numbers $1, 2, \dots, 2000$ are placed clockwise on a circle. Starting at $1$ , you delete it, keep the next ( $2$ ), delete the next ( $3$ ), keep ( $4$ ), and so on - alternately deleting and keeping around the circle - until one number remains. Which number survives?

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Josephus, step $2$ , first element deleted. Write $n=2^m+L$ with $2^m\le n$ .
$2000=1024+976$ , survivor $=2L=2\cdot976$ .

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Deleting every other number on a circle

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