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A085833
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Start at (2n+1)/4 and iterate the map x -> x*ceiling(x); sequence gives values of n for which the denominators in the orbit go from 4 to 2, instead of dropping directly to 1.
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3
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2, 3, 5, 8, 10, 11, 16, 17, 18, 19, 25, 26, 27, 28, 29, 32, 33, 34, 35, 37, 40, 42, 43, 48, 49, 50, 51, 57, 58, 59, 60, 61, 64, 65, 66, 67, 68, 72, 74, 75, 80, 82, 83, 84, 85, 89, 90, 91, 92, 93, 98, 99, 100, 104, 106, 107, 113, 114, 115, 116, 117, 121, 122, 123, 124, 125, 128, 130
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