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A099799 a(n) = least integer that begins a run of exactly n consecutive integers that can be the hypotenuse of a Pythagorean triangle. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

REFERENCES

Shanks, Daniel; Review of Consecutive Hypotenuses of Pythagorean Triangles by Albert H. Beiler, Mathematics of Computation, Vol. 22, No. 103, (July 1968), pp. 690-692. - Ant King, Feb 01 2011

LINKS

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

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

AUTHOR

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

STATUS

approved

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Last modified January 25 16:42 EST 2020. Contains 331245 sequences. (Running on oeis4.)