A108707 Minimum side in Pythagorean triangles with hypotenuse of n.

0, 0, 0, 0, 3, 0, 0, 0, 0, 6, 0, 0, 5, 0, 9, 0, 8, 0, 0, 12, 0, 0, 0, 0, 7, 10, 0, 0, 20, 18, 0, 0, 0, 16, 21, 0, 12, 0, 15, 24, 9, 0, 0, 0, 27, 0, 0, 0, 0, 14, 24, 20, 28, 0, 33, 0, 0, 40, 0, 36, 11, 0, 0, 0, 16, 0, 0, 32, 0, 42, 0, 0, 48, 24, 21, 0, 0, 30, 0, 48, 0, 18, 0, 0, 13, 0, 60, 0, 39, 54

Offset

1,5

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

a(5) = 3 as the right triangle with sides (3, 4, 5) has hypotenuse n = 5 smallest side a(5) = 3. This is the smallest side a right triangle with integer sides and hypotenuse 5 can have. - David A. Corneth, Apr 10 2021

Mathematica

f[n_]:=Block[{k=n-1, m=Sqrt[n/2], a}, While[k>m&&!IntegerQ[(a=Sqrt[n^2-k^2])], k--]; If[k<=m, 0, a]]; Table[f[n], {n, 90}]

Prog

(PARI) first(n) = {my(lh = List(), res = vector(n, i, oo)); 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)] = vecmin([res[i*(u^2+v^2)], 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

Cf. A083025, A046083, A046084, A009000, A009003, A108708.

A046080 gives the number of Pythagorean triangles with hypotenuse n.

Sequence in context: A321432 A220093 A097017 * A046775 A221787 A348070

Adjacent sequences: A108704 A108705 A108706 * A108708 A108709 A108710

Keyword

nonn

Author

Sébastien Dumortier, Jun 20 2005

Extensions

Extended by Ray Chandler, Dec 20 2011

Status

approved