A099799 a(n) = least integer that begins a run of exactly n consecutive integers that can be the hypotenuse of a Pythagorean triangle.

5, 25, 39, 50, 218, 775, 949, 673, 403, 1597, 2190, 2820, 6050, 8577, 12423, 27325, 34075, 52754, 37088, 74649, 68150, 43795, 106368, 102227, 225809, 149297, 87594, 694398, 820953, 575377, 741617, 776230, 169160, 2218014, 4506212, 2906397, 7878697, 5635624, 1884817

Offset

1,1

Comments

a(74) = 739405953; for n > 64, all other terms > 10^9. - Frank A. Stevenson, Jan 07 2024

Links

Frank A. Stevenson, Table of n, a(n) for n = 1..64

Albert H. Beiler, Review of Consecutive Hypotenuses of Pythagorean Triangles by Daniel Shanks, Mathematics of Computation, Vol. 22, No. 103, (July 1968), pp. 690-692.

Mathematica

lmt = 10^4; hyp = {5}; Do[ mn = m^2 + n^2; hyp = Join[hyp, Table[k*mn, {k, Floor[lmt/mn]}]]; hyp = Union[hyp], {n, 2, Floor[ Sqrt[lmt]]}, {m, Min[n - 1, Floor[ Sqrt[ lmt - n^2]]]}]; f[n_] := Block[{k = 1}, While[ hyp[[k]] + n - 1 != hyp[[k + n - 1]] || hyp[[k]] + n == hyp[[k + n]] || (k > 1 && hyp[[k]] == hyp[[k - 1]] + 1), k++ ]; hyp[[k]]]; Do[ Print[ f[n]], {n, 14}] (* corrected by Jason Yuen, Jun 28 2025 *)

Crossrefs

Cf. A004431, A098993.

Sequence in context: A018724 A070389 A098993 * A093534 A070388 A250314

Adjacent sequences: A099796 A099797 A099798 * A099800 A099801 A099802

Keyword

nonn

Author

Ray Chandler and Robert G. Wilson v, Nov 10 2004

Status

approved