A201006 The Isis problem: Array a(i,j) (by antidiagonals) of differences between area and perimeter of rectangle with sides (i,j).

-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 X 4 and 3 X 6".

References

Brian Greer, Dirk De Bock, and Wim Van Dooren, 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.

Links

Table of n, a(n) for n=0..104.

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

Adjacent sequences: A201003 A201004 A201005 * A201007 A201008 A201009

Keyword

sign,tabl

Author

Jean-François Alcover, Jan 08 2013

Status

approved