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 A319589 A 3 X 3 magic square with five square entries, read by rows. 1
 34969, 83521, 7585, 14641, 42025, 69409, 76465, 529, 49081 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Some magic squares of order 3 with five square entries have this parametric form: |-----------------------|-----------------------|-----------------------| | (x*y)^2 | y^4 |sqrt(z)*(3*x^2 - y^2)/2| |-----------------------|-----------------------|-----------------------| | x^4 | z | 2*z - x^4 | |-----------------------|-----------------------|-----------------------| |sqrt(z)*(3*y^2 - x^2)/2| 2*z - y^4 | 2*z - (x*y)^2 | |-----------------------|-----------------------|-----------------------| where z = (x^2 + y^2)^2/4, x and y are integers such that (x^4 - y^4 + 2*(x*y)^2)/2 is a square (e.g., x = 11 and y = 17; x = 5337 and y = 6257). This sequence presents the magic square belonging to this family and having the smallest possible magic sum (S = 126075). LINKS Table of n, a(n) for n=1..9. Index entries for sequences related to magic squares EXAMPLE The magic square is +-------+-------+-------+ | 187^2 | 17^4 | 7585 | +-------+-------+-------+ | 11^4 | 205^2 | 69409 | +-------+-------+-------+ | 76465 | 23^2 | 49081 | +-------+-------+-------+ CROSSREFS Cf. A221669, A268855. Sequence in context: A257755 A230976 A085847 * A237065 A233631 A281886 Adjacent sequences: A319586 A319587 A319588 * A319590 A319591 A319592 KEYWORD nonn,fini,full,tabf AUTHOR Arkadiusz Wesolowski, Sep 23 2018 STATUS approved

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Last modified May 31 19:41 EDT 2023. Contains 363068 sequences. (Running on oeis4.)