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

Offset

1,1

Comments

a(35), a(37), a(38)>3*10^6; a(36)=2906397, a(39)=1884817.

Links

Table of n, a(n) for n=1..34.

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 = 5*10^6; 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[ phk[[k]] + n - 1 != phk[[k + n - 1]], k++ ]; phk[[k]]]; Do[ Print[ f[n]], {n, 34}

Crossrefs

Least integer that begins a run of at least n consecutive integers that can be the hypotenuse of a Pythagorean triangle is given by A098993.

Sequence in context: A018724 A070389 A098993 * A093534 A070388 A250314

Adjacent sequences: A099796 A099797 A099798 * A099800 A099801 A099802

Keyword

nonn,more

Author

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

Status

approved