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38s and Bunches of 1s (Posted on 2017-06-30) |
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Prove every number in the sequence 38, 381, 3811, 38111, 381111, ... is composite.
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Submitted by Brian Smith
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Rating: 4.5000 (2 votes)
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Solution:
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Let S(x) denote the member of the sequence with x 1s. (x starts at 0)
If x mod 3 = 1 then S(x) is a multiple of 3.
If x mod 3 = 2 then S(x) is a multiple of 37.
If x mod 3 = 0 then S(x) is a multiple of 2333...3 where the number of 3s is equal to x.
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