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

 Submitted by Brian Smith Rating: 4.5000 (2 votes) Solution: (Hide) 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. More details can be found in the comments.

 Subject Author Date Proof Math Man 2017-07-01 21:38:12 re: Another way of seeing part of it broll 2017-06-30 23:14:23 Another way of seeing part of it Jer 2017-06-30 14:03:47 Nice problem broll 2017-06-30 10:38:00 re(2): No proof but a pattern found Charlie 2017-06-30 10:14:56 re: No proof but a pattern found chun 2017-06-30 09:42:22 No proof but a pattern found Charlie 2017-06-30 09:04:10

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