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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.

  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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionProofMath Man2017-07-01 21:38:12
Some Thoughtsre: Another way of seeing part of itbroll2017-06-30 23:14:23
Another way of seeing part of itJer2017-06-30 14:03:47
SolutionNice problembroll2017-06-30 10:38:00
re(2): No proof but a pattern foundCharlie2017-06-30 10:14:56
re: No proof but a pattern foundchun2017-06-30 09:42:22
Some ThoughtsNo proof but a pattern foundCharlie2017-06-30 09:04:10
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