A217029 Array T(i,j) read by antidiagonals, where T(i,j) is the height of i/j, that is max(|m|,|n|) with m/n = i/j and gcd(m, n) = 1.

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

Offset: 1

Author

Jean-François Alcover, Sep 24 2012

Keywords

• nonn
• nice
• tabl

Examples

			1, 2, 3, 4, 5, 6, ...
2, 1, 3, 2, 5, 3, ...
3, 3, 1, 4, 5, 2, ...
...
		

Links

• T. D. Noe, First 100 antidiagonals, flattened
• J. H. Silverman and J. H. Tate, Rational Points on Elliptic Curves, Springer 1992, p. 63.

Crossrefs

Cf. A002246.

Programs

Mathematica

t[i_, j_] := Max[ Abs[ Numerator[r = i/j]], Denominator[r]]; Table[ t[i-j+1, j], {i, 1, 14}, {j, 1, i}] // Flatten

PARI

T(i,j)=max(i/gcd(i,j),j/gcd(i,j)) \\ Charles R Greathouse IV, Sep 25 2012