

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
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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 PreService Teachers’ Ideas about Proof, in Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education 1184


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: A032446 A271563 A028949 * A107574 A241163 A053405
Adjacent sequences: A201003 A201004 A201005 * A201007 A201008 A201009


KEYWORD

sign,tabl


AUTHOR

JeanFrançois Alcover, Jan 08 2013


STATUS

approved



