A magic series is a set of distinct positive numbers which add up to the magic constant of a magic square and a magic cube, thus potentially making up lines in magic tesseracts.
So, in an n × n magic square using the numbers from 1 to n2, a magic series is a set of n distinct numbers adding up to n(n2+1)/2. For n = 2, there are just two magic series, 1+4 and 2+3. The eight magic series when n = 3 all appear in the rows, columns and diagonals of a 3 × 3 magic square.
Maurice Kraitchik gave the number of magic series up to n = 7 in Mathematical Recreations in 1942 (sequence A052456 in OEIS). In 2002, Henry Bottomley extended this up to n = 36 and independently Walter Trump up to n = 32. In 2005, Trump extended this to n = 54 (over 2×10111) while Bottomley gave an experimental approximation for the numbers of magic series:
In July 2006, Robert Gerbicz extended this sequence up to n = 150.
Famous quotes containing the words magic and/or series:
“To play safe, I prefer to accept only one type of power: the power of art over trash, the triumph of magic over the brute.”
—Vladimir Nabokov (1899–1977)
“History is nothing but a procession of false Absolutes, a series of temples raised to pretexts, a degradation of the mind before the Improbable.”
—E.M. Cioran (b. 1911)