A217029 - OEIS

%I #24 Dec 12 2015 13:11:21

%S 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,

%T 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,

%U 12,11,10,9,8,7,7,8,9,10,11,12,13,6,11,5,9

%N 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.

%H T. D. Noe, <a href="/A217029/b217029.txt">First 100 antidiagonals, flattened</a>

%H J. H. Silverman and J. H. Tate, <a href="http://dx.doi.org/10.1007/978-1-4757-4252-7">Rational Points on Elliptic Curves</a>, Springer 1992, p. 63.

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

%e 2, 1, 3, 2, 5, 3, ...

%e 3, 3, 1, 4, 5, 2, ...

%e ...

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

%o (PARI) T(i,j)=max(i/gcd(i,j),j/gcd(i,j)) \\ _Charles R Greathouse IV_, Sep 25 2012

%Y Cf. A002246.

%K nonn,nice,tabl

%O 1,2

%A _Jean-François Alcover_, Sep 24 2012