Flipping A Binary Coin

You have a fair coin with a "1" on one side and a "0" on another side. You decide to flip it until you get a string of "1"s and "0"s that is the binary representation of a number you are thinking of.

For example, if you pick the number 3, then its binary representation would be "11" and the expected number of flips to get this combination would be 6.

For what number is the expectation value for the number of flips needed to get its binary representation exactly 62?

Note: Leading zeros aren't allowed. i.e. The number 5 would be represented by 101, not 0101 nor 00101. Also, you keep flipping until you see the number anywhere in the string. i.e. You don't "start over" once you fail to see the string.

Other Expected Value Quizzes

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