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A078107 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. 3

%I

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,18,19,20,21,22,24

%N 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.

%C 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.

%C The problem originated (for n = 15) with Bernardo Recamán Santos of Colombia. The problem for necklaces is due to Joe Kisenwether.

%D _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.

%e 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).

%Y Cf. A071983, A071984, A090460, A090461.

%K nonn,fini,full

%O 1,2

%A _R. K. Guy_, Dec 06 2002

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)