A201613 - OEIS

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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

(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