A101931 Number of primitive Pythagorean triples with hypotenuse < 10^n.

1, 16, 158, 1593, 15919, 159139, 1591579, 15915492, 159154994, 1591549475, 15915494180, 159154943063, 1591549430580, 15915494309496, 159154943089963, 1591549430916326, 15915494309190251, 159154943091887752, 1591549430918979115

Offset: 1

Author

Eric W. Weisstein, Dec 21 2004

Keywords

• nonn

Comments

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

Examples

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

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..21
• D. N. Lehmer, Asymptotic evaluation of certain totient sums, Amer. J. Math. 22, 293-335, 1900.
• Eric Weisstein's World of Mathematics, Pythagorean Triple

Crossrefs

Cf. A101929, A101930.

Programs

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

Extensions

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

a(10)-a(11) from Charles R Greathouse IV, Sep 14 2012

a(12) from Charles R Greathouse IV, Oct 15 2012

a(13)-a(19) from Hiroaki Yamanouchi, Jul 14 2014