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A078107
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Numbers n such that it is not possible to arrange the numbers from 1 to n in a chain with adjacent links summing to a square.
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3
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18, 19, 20, 21, 22, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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It seems certain, on account of the valences of the underlying graph, that necklaces exist for all larger n, but this may not yet have been proved.
The problem originated (for n = 15) with Bernardo Recamán Santos of Colombia. The problem for necklaces is due to Joe Kisenwether.
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REFERENCES
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Ed Pegg Jr and W. Edwin Clark have found necklaces (and hence chains) for n = 32 onwards up to 50 and for several larger numbers.
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LINKS
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EXAMPLE
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E.g., for 15, 16 or 17, use (16-)9-7-2-14-11-5-4-12-13-3-6-10-15-1-8(-17).
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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