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%I #15 May 29 2024 13:48:43
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,18,19,20,21,22,24
%N Numbers k such that it is not possible to arrange the numbers from 1 to k 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 k, but this may not yet have been proved.
%C The problem originated (for k = 15) with Bernardo Recamán Santos of Colombia. The problem for necklaces is due to Joe Kisenwether.
%C _Ed Pegg Jr_ and _W. Edwin Clark_ have found necklaces (and hence chains) for k = 32 onwards up to 50 and for several larger numbers.
%C It has been proven that there are no more terms. See A090461 for details. - _Paolo Xausa_, May 29 2024
%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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