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| A307177
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Decimal expansion of smallest nontrivial base-10 number that contains all pairwise products of its digits as substrings.
(history;
published version)
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#19 by Alois P. Heinz at Fri Mar 29 13:07:51 EDT 2019
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#18 by Alois P. Heinz at Fri Mar 29 13:07:48 EDT 2019
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| EXAMPLE
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1012014015216242530327281835456364849.
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| STATUS
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approved
editing
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#17 by Alois P. Heinz at Fri Mar 29 13:00:30 EDT 2019
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#16 by Alois P. Heinz at Fri Mar 29 12:59:09 EDT 2019
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| KEYWORD
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nonn,cons,fini,full,base,new
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| STATUS
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approved
editing
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Discussion
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| Fri Mar 29
| 13:00
| Alois P. Heinz: base is correct here, because the decimal digits are used to define or compute this.
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#15 by Alois P. Heinz at Fri Mar 29 12:56:48 EDT 2019
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#14 by Alois P. Heinz at Fri Mar 29 12:51:24 EDT 2019
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| OFFSET
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137,4
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| KEYWORD
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nonn,basecons,fini,full,new
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| STATUS
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proposed
editing
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Discussion
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| Fri Mar 29
| 12:53
| Alois P. Heinz: the decimal expansion of a constant does not have the base keyword.
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| 12:56
| Rob Pratt: Oh, I guess offset should be 37 for this 37-digit integer.
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| 12:56
| Alois P. Heinz: you can check after approval: click the "cons" link and you should see the constant, which is an integer here.
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#13 by Rob Pratt at Fri Mar 29 12:34:33 EDT 2019
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Discussion
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| Fri Mar 29
| 12:38
| Michel Marcus: the name says : Decimal expansion of ... some number: what is this number ?
it is an integer ?
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| 12:47
| Rob Pratt: Yes, it is the integer 1012014015216242530327281835456364849
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| 12:48
| Alois P. Heinz: so it is a constant and should have keyword:cons and another offset?
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| 12:52
| Rob Pratt: Yes, cons. Not sure whether offset needs changing.
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#12 by Rob Pratt at Fri Mar 29 12:34:17 EDT 2019
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| COMMENTS
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Rob Pratt usedsolved an asymmetric traveling salesman problem (ATSP) formulation on 38 nodes to minimizefind the minimum number of digits, which turns out to be 37, and then usedsolved a sequence of integer linear programming problems (minimizing one digit at a time from left to right) to find the minimum such 37-digit number.
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#11 by Rob Pratt at Fri Mar 29 12:32:24 EDT 2019
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| COMMENTS
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Rob Pratt used an asymmetric atraveling TSPsalesman problem (ATSP) formulation on 38 nodes to minimize the number of digits, which turns out to be 37, and then used a sequence of integer linear programming problems (minimizing one digit at a time from left to right) to find the minimum such 37-digit number.
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| STATUS
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approved
editing
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#10 by N. J. A. Sloane at Thu Mar 28 00:39:40 EDT 2019
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