A107142 Primes of the form x^2 + 36y^2.

37, 61, 157, 193, 313, 349, 373, 397, 433, 577, 601, 613, 661, 673, 769, 853, 877, 937, 997, 1021, 1069, 1201, 1297, 1321, 1429, 1549, 1657, 1693, 1741, 1789, 1801, 1861, 1933, 1993, 2053, 2137, 2269, 2293, 2389, 2437, 2473, 2521, 2593, 2749

Offset: 1

Author

T. D. Noe, May 13 2005

Keywords

• nonn
• easy

Comments

Discriminant = -144. See A107132 for more information.

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

References

• J. W. L. Glaisher, On the square of Euler's series, Proc. London Math. Soc., 21 (1889), 182-194.

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• S. R. Finch, Powers of Euler's q-Series, (arXiv:math.NT/0701251).
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Programs

Mathematica

QuadPrimes2[1, 0, 36, 10000] (* see A106856 *)

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