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- 114354
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- 2005-9-23
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- 1970-1-1
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X20 - X19 = (2 * X19 - 1) - X19 = X19 - 1 = (2 * X18 - 1) - 1 = 2 * (2 * X17 - 1) - 2 = 2 * (2 * (2 * X16 - 1) - 1) - 2 = 2 * 2 * 2 * X16 - 2 * 2 - 2 - 1 - 1 = 2^18 * X1 - (2^17 + 2^16 + ... + 2^2 + 2^1 + 2^0) - 1 = 2^18 * 3 - sum of(2^k) where k goes from 0 to 17 (see note) - 1 = 2^18 * 3 - (2^18 - 1) / (2 - 1) - 1 = 2^18 * 3 - 2^18 + 1 - 1 = 2^18 * 2 = 2^19 |
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