|
%I #25 Feb 09 2017 14:34:47
%S 13,73,97,109,181,229,241,277,337,409,421,457,541,709,733,757,829,
%T 1009,1033,1093,1117,1129,1153,1213,1237,1249,1381,1453,1489,1597,
%U 1609,1621,1669,1753,1777,1873,2017,2029,2089,2113,2161,2221,2281
%N Primes of the form 4x^2 + 9y^2.
%C Discriminant = -144. See A107132 for more information.
%C These appear to be the same as Glaisher's 1889 list of primes == 1 mod 12 that have "negative character". - _N. J. A. Sloane_, Jul 30 2015
%D J. W. L. Glaisher, On the square of Euler's series, Proc. London Math. Soc., 21 (1889), 182-194.
%H Vincenzo Librandi and Ray Chandler, <a href="/A107141/b107141.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]
%H S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0701251">Powers of Euler's q-Series</a>, (arXiv:math.NT/0701251).
%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%t QuadPrimes2[4, 0, 9, 10000] (* see A106856 *)
%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\4), w=4*x^2; for(y=1, sqrtint((lim-w)\9), if(isprime(t=w+9*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 09 2017
%K nonn,easy
%O 1,1
%A _T. D. Noe_, May 13 2005
|
