A201613 Primes of the form p^2 + 2q^2 with p and q odd primes.

43, 59, 67, 107, 139, 251, 307, 347, 379, 547, 587, 859, 1699, 1867, 1931, 3371, 3499, 3739, 4507, 5059, 5347, 6907, 6971, 7451, 10091, 10627, 10667, 11467, 12491, 18787, 20411, 21227, 22907, 29947, 32059, 32779, 37547, 38651, 39619, 49307, 49747, 53147, 55787

Offset: 1

Author

Zak Seidov, Dec 03 2011

Keywords

• nonn

Comments

One of primes p, q must be 3, hence we have two sets of primes: 9+2*p^2 and p^2+18 with p > 3.

Note that if we allow 2 for p or q then there is another "set" of primes of the form p^2+8 (q=2) with odd prime p -- this set contains only the prime 17=3^2+8.

Examples

			43=5^2+2*3^2, 59=3^2+2*5^2, 67=7^2+2*3^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A260553 and of A154777.

Programs

PARI

list(lim)=my(v=List(),t); forprime(p=5,sqrtint(lim\1-18), if(isprime(t=p^2+18), listput(v,t))); forprime(q=5,sqrtint((lim-9)\2), if(isprime(t=2*q^2+9), listput(v,t))); Set(v) \\ Charles R Greathouse IV, Aug 26 2015

Extensions

Corrected by Charles R Greathouse IV, Aug 26 2015