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For the rest of this century 2017 will be repeated exactly in 2023, 2034, 2045, 2051, 2062, 2073, 2079 and 2090.
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Any irrational number can be approximated by decimals. You can never write it exactly, since there are an infinite number of decimals, and these don't repeat.
The calendar for the year 1987 will repeat exactly in the year 2018. This is because the Gregorian calendar repeats every 28 years. The calendar for any specific year will repeat in the year that is a multiple of 28 years later.
When you recite something you simply speak it out loud, whether it is a poem or a speech or something else. Recounting something is recollecting out loud something that has actually happened to yourself.