A107141 Primes of the form 4x^2 + 9y^2.

13, 73, 97, 109, 181, 229, 241, 277, 337, 409, 421, 457, 541, 709, 733, 757, 829, 1009, 1033, 1093, 1117, 1129, 1153, 1213, 1237, 1249, 1381, 1453, 1489, 1597, 1609, 1621, 1669, 1753, 1777, 1873, 2017, 2029, 2089, 2113, 2161, 2221, 2281

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 "negative 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[4, 0, 9, 10000] (* see A106856 *)

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