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URL: https://oeis.org/A101931

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A101931
Number of primitive Pythagorean triples with hypotenuse < 10^n.
13
1, 16, 158, 1593, 15919, 159139, 1591579, 15915492, 159154994, 1591549475, 15915494180, 159154943063, 1591549430580, 15915494309496, 159154943089963, 1591549430916326, 15915494309190251, 159154943091887752, 1591549430918979115
OFFSET
1,2
COMMENTS
The ratio a(n)/10^n as n->inf is 1/(2*Pi) = 0.15915... (Lehmer). - Tito Piezas III, Aug 11 2006
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
EXAMPLE
a(1)=1 because there is one primitive solution (a,b,c) as (3,4,5) with c<10^1.
PROG
(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
CROSSREFS
Sequence in context: A320548 A211831 A036973 * A220630 A041005 A180798
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 21 2004
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
STATUS
approved