OFFSET
1,1
COMMENTS
REFERENCES
Albert H. Beiler, Recreations In The Theory Of Numbers, Chapter XIV, The Eternal Triangle, Dover Publications Inc., New York, 1964, pp. 104-134.
W. Sierpinski, Pythagorean Triangles, Dover Publications, Inc., Mineola, New York, 2003.
LINKS
Shujing Lyu, Table of n, a(n) for n = 1..5000
Robert Recorde, The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the extraction of rootes; the cossike practise, with the rule of equation; and the workes of Surde Nombers, London, 1557. See p. 57.
EXAMPLE
As the first four Pythagorean triples (ordered by increasing A) are (3,4,5), (5,12,13), (6,8,10) and (7,24,25), then a(1)=4, a(2)=12, a(3)=8 and a(4)=24.
MATHEMATICA
PythagoreanTriplets[n_]:=Module[{t={{3, 4, 5}}, i=4, j=5}, While[i<n, h=Sqrt[i^2+j^2]; If[IntegerQ[h] && j<n, AppendTo[t, {i, j, h}]]; If[j<n, j++, i++; j=i+1]]; t]; k=20; data1=PythagoreanTriplets[2k^2+2k+1]; data2=Select[data1, #[[1]]<=2k+1 &]; #[[2]] &/@data2
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Ant King, Feb 17 2009
STATUS
approved