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A266954 Primes of the form p = a^2 + b^2 where neither |a+b| nor |a-b| is prime.

%I A266954 #9 Aug 12 2022 19:26:32
%S A266954 41,113,313,353,613,653,677,761,857,977,1013,1201,1301,1373,1553,1613,
%T A266954 1733,1877,1913,2113,2153,2213,2237,2273,2297,2333,2381,2477,2657,
%U A266954 2693,2713,3137,3313,3329,3413,3581,3593,3613,3833,4013,4157,4253,4373,4397,4481
%N A266954 Primes of the form p = a^2 + b^2 where neither |a+b| nor |a-b| is prime.
%H A266954 Robert Israel, <a href="/A266954/b266954.txt">Table of n, a(n) for n = 1..10000</a>
%H A266954 Mathematics Stack Exchange, <a href="http://math.stackexchange.com/questions/1602695/a-curious-pattern-on-primes-congruent-to-1-mod-4">A curious pattern on primes congruent to 1 mod 4</a>
%p A266954 filter:= proc(q) local t,p;
%p A266954       if not isprime(q) then return false fi;
%p A266954       t:= op(op(1,GaussInt:-GIfactor(q)));
%p A266954     p:= [abs(Re(t)+Im(t)),abs(Re(t)-Im(t))];
%p A266954     not isprime(p[1]) and not isprime(p[2])
%p A266954 end proc:
%p A266954 select(filter, [seq(i, i=1..10000, 4)]);
%t A266954 lst = {}; Do[If[PrimeQ[a^2 + b^2] && ! PrimeQ[a + b] && ! PrimeQ[a - b], AppendTo[lst, a^2 + b^2]], {a, 2, 67}, {b, a -1}]; Take[ Union@ lst, 50] (* _Robert G. Wilson v_, Jan 06 2016 *)
%K A266954 nonn
%O A266954 1,1
%A A266954 _Robert Israel_, Jan 06 2016