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%I A101931 #26 Jan 10 2016 01:33:13
%S A101931 1,16,158,1593,15919,159139,1591579,15915492,159154994,1591549475,
%T A101931 15915494180,159154943063,1591549430580,15915494309496,
%U A101931 159154943089963,1591549430916326,15915494309190251,159154943091887752,1591549430918979115
%N A101931 Number of primitive Pythagorean triples with hypotenuse < 10^n.
%C A101931 The ratio a(n)/10^n as n->inf is 1/(2*Pi) = 0.15915... (Lehmer). - _Tito Piezas III_, Aug 11 2006
%H A101931 Hiroaki Yamanouchi, <a href="/A101931/b101931.txt">Table of n, a(n) for n = 1..21</a>
%H A101931 D. N. Lehmer, <a href="http://www.jstor.org/stable/2369728">Asymptotic evaluation of certain totient sums</a>, Amer. J. Math. 22, 293-335, 1900.
%H A101931 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>
%e A101931 a(1)=1 because there is one primitive solution (a,b,c) as (3,4,5) with c<10^1.
%o A101931 (PARI) a(n)=my(t,lim=10^n);for(m=2,sqrtint(lim-1),forstep(n=1+m%2,min(sqrtint(lim-m^2),m-1),2,if(gcd(m,n)==1,t++)));t \\ _Charles R Greathouse IV_, Sep 13 2012
%Y A101931 Cf. A101929, A101930.
%K A101931 nonn
%O A101931 1,2
%A A101931 _Eric W. Weisstein_, Dec 21 2004
%E A101931 More terms from Jan Feitsma and Bart Dopheide (dopheide(AT)fmf.nl), Mar 10 2005
%E A101931 a(10)-a(11) from _Charles R Greathouse IV_, Sep 14 2012
%E A101931 a(12) from _Charles R Greathouse IV_, Oct 15 2012
%E A101931 a(13)-a(19) from _Hiroaki Yamanouchi_, Jul 14 2014

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