A101931 - OEIS

%I #26 Jan 10 2016 01:33:13

%S 1,16,158,1593,15919,159139,1591579,15915492,159154994,1591549475,

%T 15915494180,159154943063,1591549430580,15915494309496,

%U 159154943089963,1591549430916326,15915494309190251,159154943091887752,1591549430918979115

%N Number of primitive Pythagorean triples with hypotenuse < 10^n.

%C The ratio a(n)/10^n as n->inf is 1/(2*Pi) = 0.15915... (Lehmer). - _Tito Piezas III_, Aug 11 2006

%H Hiroaki Yamanouchi, <a href="/A101931/b101931.txt">Table of n, a(n) for n = 1..21</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PythagoreanTriple.html">Pythagorean Triple</a>

%e a(1)=1 because there is one primitive solution (a,b,c) as (3,4,5) with c<10^1.

%o (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 Cf. A101929, A101930.

%K nonn

%O 1,2

%A _Eric W. Weisstein_, Dec 21 2004

%E More terms from Jan Feitsma and Bart Dopheide (dopheide(AT)fmf.nl), Mar 10 2005

%E a(10)-a(11) from _Charles R Greathouse IV_, Sep 14 2012

%E a(12) from _Charles R Greathouse IV_, Oct 15 2012

%E a(13)-a(19) from _Hiroaki Yamanouchi_, Jul 14 2014