32,3

It is unknown whether a circular permutation of the numbers 1 to n exists such that the sum of any two consecutive numbers is a cube.

According to Rivera's Puzzle 311, the smallest n for which a cubic loop exists is 473. - T. D. Noe (noe(AT)sspectra.com), Nov 26 2007

Carlos Rivera, Puzzle 311: Sum to a cube

There is only one possible square loop of minimum length, which is: (32, 4, 21, 28, 8, 1, 15, 10, 26, 23, 2, 14, 22, 27, 9, 16, 20, 29, 7, 18, 31, 5, 11, 25, 24, 12, 13, 3, 6, 30, 19, 17) so a(32)=1.

Cf. A071983, A112663.

Sequence in context: A034264 A051946 A114030 this_sequence A101094 A014470 A048366

Adjacent sequences: A071981 A071982 A071983 this_sequence A071985 A071986 A071987

nice,nonn

William Rex Marshall (w.r.marshall(AT)actrix.co.nz), Jun 16 2002