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# Magic Series

A set of distinct numbers taken from the interval form a magic series if their sum is the th magic constant

(Kraitchik 1942, p. 143). The numbers of magic series of orders , 2, ..., are 1, 2, 8, 86, 1394, ... (OEIS A052456). The following table gives the first few magic series of small order.

 magic series 1 2 , 3 , , , , , , ,

If the sum of the th powers of these number is the magic constant of degree for all , then they are said to form a th order multimagic series. Here, the magic constant of degree is defined as times the sum of the first th powers,

where is a harmonic number of order .

Magic Constant, Magic Square, Multimagic Series

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## References

Kraitchik, M. "Magic Series." §7.13.3 in Mathematical Recreations. New York: W. W. Norton, pp. 143 and 183-186, 1942.Sloane, N. J. A. Sequence A052456 in "The On-Line Encyclopedia of Integer Sequences."

Magic Series

## Cite this as:

Weisstein, Eric W. "Magic Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MagicSeries.html