A101929 Number of Pythagorean triples with hypotenuse < 10^n.

1, 50, 878, 12467, 161431, 1980636, 23471468, 271360645, 3080075423, 34465432849, 381301109908, 4179478903380, 45459467009955, 491241450001314, 5278882299478781, 56453500988940599, 601181789833245614, 6378285697775544212

Offset: 1

Author

Eric W. Weisstein, Dec 21 2004

Keywords

• nonn

Comments

There seems to be a relation between A101930 and this sequence: A101930(n) = n + a(n). - Jan Feitsma and Bart Dopheide (dopheide(AT)fmf.nl), Mar 10 2005

A101930(n) - a(n) = A046080(10^n). The formula listed for A046080 supports the relation of Jan Feitsma and Bart Dopheide: A046080(10^n) = n. - Frank Marcoline (fvmarcoline(AT)gmail.com), Dec 10 2008

Links

• Eric Weisstein's World of Mathematics, Pythagorean Triple

Crossrefs

Cf. A101930.

Programs

PARI

a(n)=my(t, lim=10^n-1); 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+=lim\(m^2+n^2)))); t \\ Charles R Greathouse IV, Sep 15 2012

Formula

a(n) = A101930(n) - n. - Robert G. Wilson v, Mar 20 2014

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 15 2012

a(12)-a(17) from Hiroaki Yamanouchi, Jul 14 2014

a(18) from Matan M. Atzmoni, Feb 04 2023