A266954 - OEIS

%I #9 Aug 12 2022 19:26:32

%S 41,113,313,353,613,653,677,761,857,977,1013,1201,1301,1373,1553,1613,

%T 1733,1877,1913,2113,2153,2213,2237,2273,2297,2333,2381,2477,2657,

%U 2693,2713,3137,3313,3329,3413,3581,3593,3613,3833,4013,4157,4253,4373,4397,4481

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

%H Robert Israel, <a href="/A266954/b266954.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 filter:= proc(q) local t,p;

%p       if not isprime(q) then return false fi;

%p       t:= op(op(1,GaussInt:-GIfactor(q)));

%p     p:= [abs(Re(t)+Im(t)),abs(Re(t)-Im(t))];

%p     not isprime(p[1]) and not isprime(p[2])

%p end proc:

%p select(filter, [seq(i, i=1..10000, 4)]);

%t 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 nonn

%O 1,1

%A _Robert Israel_, Jan 06 2016