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MATH / At a competition with N players, the number of players given elite status is equal to 2^(1+⌊log₂(N−1)⌋)−N. Suppose that 19 players are given elite status. What is the sum of the tw…

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problem

At a competition with NN players, the number of players given elite status is equal to 21+⌊log2(N−1)⌋−N2^{1+\lfloor \log_{2} (N-1) \rfloor}-N. Suppose that 1919 players are given elite status. What is the sum of the two smallest possible values of NN?
Plain-text mathematical notation (without MathML)
At a competition with N players, the number of players given elite status is equal to 2^(1+⌊log₂(N−1)⌋)−N. Suppose that 19 players are given elite status. What is the sum of the two smallest possible values of N?
Original LaTeX notation
At a competition with $N$ players, the number of players given elite status is equal to $2^{1+\lfloor \log_{2} (N-1) \rfloor}-N$. Suppose that $19$ players are given elite status. What is the sum of the two smallest possible values of $N$?

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
01d1ae60-864d-552f-a68c-509c8abed372
task_key
intermediate~5falgebra--test--01d1ae60-864d-552f-a68c-509c8abed372
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import