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

1,2

Links

T. D. Noe, First 100 antidiagonals, flattened

J. H. Silverman and J. H. Tate, Rational Points on Elliptic Curves, Springer 1992, p. 63.

Example

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

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

Prog

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

Crossrefs

Cf. A002246.

Sequence in context: A338573 A113881 A072030 * A331886 A205456 A080045

Adjacent sequences: A217026 A217027 A217028 * A217030 A217031 A217032

Keyword

nonn,nice,tabl

Author

Jean-François Alcover, Sep 24 2012

Status

approved