

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
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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. 690692.  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



