A set of n distinct numbers taken from the interval [1, n^2] form a magic series if their sum is the nth magic constant M_n = 1/2 n(n^2 + 1) (Kraitchik 1942, p. 143). The numbers of magic series of orders n = 1, 2, ..., are 1, 2, 8, 86, 1394, ... (OEIS A052456). The following table gives the first few magic series of small order. n | magic series 1 | {1} 2 | {1, 4}, {2, 3} 3 | {1, 5, 9}, {1, 6, 8}, {2, 4, 9}, {2, 5, 8}, {2, 6, 7}, {3, 4, 8}, {3, 5, 7}, {4, 5, 6}

magic constant | magic square | multimagic series