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A201006
The Isis problem : Array a(i,j) (by antidiagonals) of differences between area and perimeter of rectangle with sides (i,j).
0
-3, -4, -4, -5, -4, -5, -6, -4, -4, -6, -7, -4, -3, -4, -7, -8, -4, -2, -2, -4, -8, -9, -4, -1, 0, -1, -4, -9, -10, -4, 0, 2, 2, 0, -4, -10, -11, -4, 1, 4, 5, 4, 1, -4, -11, -12, -4, 2, 6, 8, 8, 6, 2, -4, -12, -13, -4, 3, 8, 11, 12, 11, 8, 3, -4, -13, -14, -4, 4, 10, 14, 16, 16, 14, 10, 4, -4, -14, -15, -4, 5, 12, 17, 20, 21, 20, 17, 12, 5, -4, -15, -16, -4, 6, 14, 20, 24, 26, 26, 24, 20, 14, 6, -4, -16
OFFSET
0,1
COMMENTS
Quotation from the reference: "Which rectangles with integer sides (in some unit) have the property that the area and the perimeter are (numerically) equal? It is not difficult to prove that there are precisely two rectangles with integer sides (in some unit of length) that have the property that the area and perimeter are numerically equal, namely 4 × 4 and 3 × 6".
REFERENCES
Greer, Brian & Bock, Dirk De & Dooren, Wim Van, The ISIS Problem and Pre-Service Teachers’ Ideas about Proof, in Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education 1-184
MATHEMATICA
a[i_, j_] := i*j - 2i - 2j; Table[a[i - j + 1, j], {i, 1, 14}, {j, 1, i}] // Flatten
CROSSREFS
Sequence in context: A271563 A342938 A028949 * A107574 A341730 A241163
KEYWORD
sign,tabl
AUTHOR
STATUS
approved