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A249750
Number of primitive Pythagorean triples with perimeter < 10^n.
3
0, 7, 70, 703, 7026, 70229, 702309, 7023027, 70230484, 702304875, 7023049293, 70230492763, 702304928492, 7023049277919, 70230492773355, 702304927727064, 7023049277265686, 70230492772676557
OFFSET
1,2
COMMENTS
The ratio a(n)/10^n as n->inf is log(2)/Pi^2 = 0.70230... (Lehmer - A118858).
LINKS
D. N. Lehmer, Asymptotic evaluation of certain totient sums, Amer. J. Math. 22, 293-335, 1900.
Eric Weisstein's World of Mathematics, Primitive Pythagorean Triple
EXAMPLE
a(2)=7 because there are 7 primitive solutions (a,b,c) with a+b+c<10^2.
(3,4,5),(5,12,13),(8,15,17),(7,24,25),(20,21,29),(12,35,37),(9,40,41)
MATHEMATICA
lst1 = {}; Do[If[GCD[m, n]==1&&m<n&&OddQ[m+n], AppendTo[lst1, 2n(n+m)]], {n, 5000}, {m, n}]; Table[Length@Select[lst1, #<10^n &], {n, 10}]
CROSSREFS
Cf. A118858.
Sequence in context: A015251 A299870 A196662 * A144848 A292841 A180902
KEYWORD
nonn,more
AUTHOR
Frank M Jackson, Nov 04 2014
EXTENSIONS
a(8)-a(18) from Hiroaki Yamanouchi, Nov 17 2014
STATUS
approved