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 A201613 Primes of the form p^2 + 2q^2 with p and q odd primes. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 EXAMPLE 43=5^2+2*3^2, 59=3^2+2*5^2, 67=7^2+2*3^2. PROG (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 CROSSREFS Subsequence of A260553 and of A154777. Sequence in context: A166491 A127880 A078132 * A115404 A033223 A215538 Adjacent sequences: A201610 A201611 A201612 * A201614 A201615 A201616 KEYWORD nonn AUTHOR Zak Seidov, Dec 03 2011 EXTENSIONS Corrected by Charles R Greathouse IV, Aug 26 2015 STATUS approved

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Last modified December 9 09:12 EST 2023. Contains 367690 sequences. (Running on oeis4.)