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

0,2

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

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 *)

Crossrefs

Except for offset, same as A046112.

Sequence in context: A036156 A097756 A046112 * A032534 A036151 A271380

Adjacent sequences: A006336 A006337 A006338 * A006340 A006341 A006342

Keyword

nonn

Author

David W. Wilson

Status

approved