A201613 - OEIS

%I #18 Oct 30 2018 10:31:02

%S 43,59,67,107,139,251,307,347,379,547,587,859,1699,1867,1931,3371,

%T 3499,3739,4507,5059,5347,6907,6971,7451,10091,10627,10667,11467,

%U 12491,18787,20411,21227,22907,29947,32059,32779,37547,38651,39619,49307,49747,53147,55787

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

%C 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.

%C 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.

%H Charles R Greathouse IV, <a href="/A201613/b201613.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (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

%Y Subsequence of A260553 and of A154777.

%K nonn

%O 1,1

%A _Zak Seidov_, Dec 03 2011

%E Corrected by _Charles R Greathouse IV_, Aug 26 2015