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- Magic_series abstract "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.In 2013 Dirk Kinnaes was able to exploit his insight that the magic series could be related to the volume of a polytope. Walter Trump used this new approach to extend the sequence up to n = 1000.Mike Quist showed that the exact second-order count has a multiplicative factor of equivalent to a denominator of Richard Schroeppel in 1973 was able to give the complete enumeration of the order 5 magic square at 275,305,224. This recent magic series work gives hope that the relationship between the magic series and the magic square may provide an exact count for order 6 or order 7 magic squares. Consider an intermediate structure that lies in complexity between the magic series and the magic square. It might be described as an amalgamation of 4 magic series that have only one unique common integer. This structure forms the two major diagonals and the central row and column for an odd order magic square. Building blocks such as these could be the way forward.".
- Magic_series wikiPageExternalLink 1307.0124v1.pdf.
- Magic_series wikiPageExternalLink magic.txt.
- Magic_series wikiPageExternalLink index.html.
- Magic_series wikiPageID "1766665".
- Magic_series wikiPageRevisionID "565510725".
- Magic_series hasPhotoCollection Magic_series.
- Magic_series subject Category:Magic_squares.
- Magic_series type Abstraction100002137.
- Magic_series type Arrangement107938773.
- Magic_series type Array107939382.
- Magic_series type Group100031264.
- Magic_series type MagicSquare108269707.
- Magic_series type MagicSquares.
- Magic_series type Matrix108267640.
- Magic_series type SquareMatrix108268085.
- Magic_series comment "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.".
- Magic_series label "Magic series".
- Magic_series sameAs m.05v7b3.
- Magic_series sameAs Q6730970.
- Magic_series sameAs Q6730970.
- Magic_series sameAs Magic_series.
- Magic_series wasDerivedFrom Magic_series?oldid=565510725.
- Magic_series isPrimaryTopicOf Magic_series.