A107142 - OEIS

%I #22 Feb 09 2017 14:35:58

%S 37,61,157,193,313,349,373,397,433,577,601,613,661,673,769,853,877,

%T 937,997,1021,1069,1201,1297,1321,1429,1549,1657,1693,1741,1789,1801,

%U 1861,1933,1993,2053,2137,2269,2293,2389,2437,2473,2521,2593,2749

%N Primes of the form x^2 + 36y^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 "positive 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="/A107142/b107142.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[1, 0, 36, 10000] (* see A106856 *)

%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\1), w=x^2; for(y=1, sqrtint((lim-w)\36), if(isprime(t=w+36*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