A006339 Least hypotenuse of n distinct Pythagorean triangles.

1, 5, 25, 125, 65, 3125, 15625, 325, 390625, 1953125, 1625, 48828125, 4225, 1105, 6103515625, 30517578125, 40625, 21125, 3814697265625, 203125, 95367431640625, 476837158203125, 5525, 11920928955078125, 274625, 5078125, 1490116119384765625, 528125, 25390625, 186264514923095703125

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 0..1438 (a(1439) exceeds 1000 digits).
• Eric Weisstein's World of Mathematics, Circle Lattice Points
• Eric Weisstein's World of Mathematics, Pythagorean Triple

Crossrefs

Except for offset, same as A046112.

Programs

Mathematica

oneModFourPrimes[1] = 5;
oneModFourPrimes[n_] := oneModFourPrimes[n] = NestWhile[NextPrime, NextPrime[oneModFourPrimes[n - 1]], Mod[#, 4] != 1 & ];
factorizations[1, limit_] = {{}};
factorizations[n_, limit_] := factorizations[n, limit] = Join @@ Table[Prepend[#, d]& /@ factorizations[n/d, d], {d, Select[Rest[Divisors[n]], # <= limit & ]}];
leastHypotenuse[n_] := Min[(Times @@ (Array[oneModFourPrimes, Length[#]]^((# - 1)/2)) & ) /@ factorizations[2*n + 1, 2*n + 1]];
Array[leastHypotenuse, 30, 0]
(* Albert H. Mao, Jan 06 2012 *)