A355242 - OEIS

A355242

T(w,h) is the minimum integer slope >= 1 that can be chosen as orientation of a w X h rectangle such that the upper bound for the minimum number of covered grid points A354702(w,d) can be achieved by a suitable translation of the rectangle, where T(w,h) and A354702 are triangles read by rows. T(w,h) = -1 if no integer slope satisfying this condition exists.

1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 2, 1, 3, 3, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,6

COMMENTS

T(17,13) = -1 is the first occurrence of the situation that it is not possible to reach the upper limit A354702(17,13) = 215 with a rectangle whose long side has an integer slope. (17 X 13)-rectangles with integer slope cannot cover less than 216 grid points. To achieve 215 grid points requires a slope of 3/2, i.e. A355241(17,13) = 3. See the linked file for related illustrations.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..210, rows 1..20 of triangle, flattened

Hugo Pfoertner, (17 X 13)-rectangles with minimum number of covered grid points

EXAMPLE

The triangle begins:

\ h 1 2 3 4 5 6 7 8 9 10 11 12 13

w \ --------------------------------------

1 | 1; | | | | | | | | | | | |

2 | 1, 1; | | | | | | | | | | |

3 | 1, 1, 2; | | | | | | | | | |

4 | 1, 1, 2, 1; | | | | | | | | |

5 | 1, 1, 2, 1, 3; | | | | | | | |