|
|
A078107
|
|
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.
|
|
3
|
|
|
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)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
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.
The problem originated (for k = 15) with Bernardo Recamán Santos of Colombia. The problem for necklaces is due to Joe Kisenwether.
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.
It has been proven that there are no more terms. See A090461 for details. - Paolo Xausa, May 29 2024
|
|
LINKS
|
|
|
EXAMPLE
|
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).
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,fini,full
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|