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A108708
Maximum side length in Pythagorean triangles with hypotenuse n.
2
0, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 12, 0, 12, 0, 15, 0, 0, 16, 0, 0, 0, 0, 24, 24, 0, 0, 21, 24, 0, 0, 0, 30, 28, 0, 35, 0, 36, 32, 40, 0, 0, 0, 36, 0, 0, 0, 0, 48, 45, 48, 45, 0, 44, 0, 0, 42, 0, 48, 60, 0, 0, 0, 63, 0, 0, 60, 0, 56, 0, 0, 55, 70, 72, 0, 0, 72, 0, 64, 0, 80, 0, 0, 84, 0, 63, 0
OFFSET
1,5
LINKS
EXAMPLE
a(5) is 4 as the maximum side (other than the hypotenuse) a right triangle with integer sides and hypotenuse 5 can have.
MATHEMATICA
f[n_] := Block[{k = n - 1, m = Sqrt[n/2]}, While[k > m && !IntegerQ[Sqrt[n^2 - k^2]], k-- ]; If[k <= m, 0, k]]; Table[ f[n], {n, 90}] (* Robert G. Wilson v, Jun 21 2005 *)
PROG
(PARI) first(n) = {my(lh = List(), res = vector(n)); for(u = 2, sqrtint(n), for(v = 1, u, if (u^2+v^2 > n, break); if ((gcd(u, v) == 1) && (0 != (u-v)%2), for (i = 1, n, if (i*(u^2+v^2) > n, break); listput(lh, i*(u^2+v^2)); res[i*(u^2+v^2)] = max(res[i*(u^2+v^2)], max(i*(u^2 - v^2), i*2*u*v)); ); ); ); ); for(i = 1, n, if(res[i] == oo, res[i] = 0)); res } \\ David A. Corneth, Apr 10 2021, adapted from A009000
CROSSREFS
A046080 gives the number of Pythagorean triangles with hypotenuse n.
Sequence in context: A276580 A331437 A351572 * A290322 A274948 A005925
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Jun 21 2005
STATUS
approved