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38s and Bunches of 1s (Posted on 2017-06-30) Difficulty: 3 of 5
Prove every number in the sequence 38, 381, 3811, 38111, 381111, ... is composite.

See The Solution Submitted by Brian Smith    
Rating: 4.5000 (2 votes)

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re: No proof but a pattern found | Comment 2 of 7 |
(In reply to No proof but a pattern found by Charlie)

More analysis of the pattern

Every third one divisible by 3 is easy to see by adding the digits.

The one after that is always 37*103, 37*103003, 37*103003003, 37*103003003003,...

The one next is always 23*1657, 233*163567, 2333*16335667, 23333*1633356667, 233333*163333566667,...

Probably we can get a proof by the pattern of the latter to situations.


  Posted by chun on 2017-06-30 09:42:22
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