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Search: id:A078107
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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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+0
4
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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; listen)
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OFFSET
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1,2
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COMMENT
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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 Recaman Santos of Colombia. The problem for necklaces is due to Joe Kisenwether.
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REFERENCES
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Ed Pegg and Edwin Clark have found necklaces (and hence chains) for n = 32 onwards up to 50 and for several larger numbers.
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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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Cf. A071983, A071984, A090460, A090461.
Sequence in context: A023783 A166535 A039698 this_sequence A072089 A072088 A023768
Adjacent sequences: A078104 A078105 A078106 this_sequence A078108 A078109 A078110
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KEYWORD
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nonn,fini,full
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AUTHOR
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R. K. Guy, Dec 06 2002
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