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Консультация № 202708
04.05.2022, 11:24
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Здравствуйте! Прошу помощи в следующем вопросе:
В последовательности чисел 1,501,751,876,438,… каждое число, кроме первого, равно половине предыдущего, если предыдущее чётно, и половине предыдущего числа, увеличенного на 1001, в противном случае. Верно ли, что в этой последовательности встретятся все натуральные числа от 1 до 1000?
Согласно описанному в задаче алгоритму, мной найден цикл, который включает в себя повторяющуюся последовательность из 62 чисел. Нужно доказательство с т.з. математики.
В последовательности чисел 1,501,751,876,438,… каждое число, кроме первого, равно половине предыдущего, если предыдущее чётно, и половине предыдущего числа, увеличенного на 1001, в противном случае. Верно ли, что в этой последовательности встретятся все натуральные числа от 1 до 1000?
Согласно описанному в задаче алгоритму, мной найден цикл, который включает в себя повторяющуюся последовательность из 62 чисел. Нужно доказательство с т.з. математики.
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