[seqfan] ApSimon's Mints counterexample

Tanya Khovanova tanyakh at yahoo.com
Wed Jun 18 17:39:07 CEST 2014

Dear SeqFans,

Konstantin Knop posted an example for 6 mints using 30 coins as a comment for my blog post:

P=(0,1,1,2,4,8) and Q=(9,6,1,1,1,1) ->  sum = 9+6+1+2+4+8=30.

I checked it. It gives different ratios.

That means Konstantin proved that the sequence http://oeis.org/A007673
is wrong.

BTW, someone should checked 4 and 5 mints. ApSimon gives two solutions for 4 mints with 8 coins: P=(0,1,2,3), Q=(1,2,2,0) and P=(0,1,1,4), Q=(2,0,1,1). And one solution for 5 coins with 15 mints: P=(1,0,1,4,5), Q=(1,2,2,5,0). He claims that he proved optimality, but it is not included in the book.


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