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A349202 Numbers k of the form (x + y)*(x^2 + y^2) such that (x + y) and (x^2 + y^2) are primes.

%I A349202 #11 Dec 25 2021 02:37:14
%S A349202 4,15,65,85,203,259,671,803,1111,1157,1261,1417,2533,2669,3439,3667,
%T A349202 3893,4369,4579,5567,6187,6371,8027,9407,12209,12557,13369,16151,
%U A349202 16771,17429,18383,18589,20491,21257,21731,26233,28453,29489,30673,34973,36121,36889
%N A349202 Numbers k of the form (x + y)*(x^2 + y^2) such that (x + y) and (x^2 + y^2) are primes.
%H A349202 Peter Luschny, <a href="/A349202/b349202.txt">Table of n, a(n) for n = 1..1200</a>
%F A349202 Intersection of A001358 and A348897.
%e A349202 1157 is in this sequence because 1157 = (5 + 8)*(5^2 + 8^2) = 13*89.
%o A349202 (Julia) # Returns the terms less than or equal to b^3.
%o A349202 using Nemo
%o A349202 function A349202List(b)
%o A349202     b3 = b^3; R = Int[]
%o A349202     for n in 1:b
%o A349202         for k in 0:n
%o A349202             a = (n + k) * (n^2 + k^2)
%o A349202             a > b3 && break
%o A349202             isprime(n+k) && isprime(n^2 + k^2) && push!(R, a)
%o A349202     end end
%o A349202 sort(R) end
%o A349202 A349202List(34) |> println
%Y A349202 Cf. A001358, A348897.
%K A349202 nonn
%O A349202 1,1
%A A349202 _Peter Luschny_, Nov 11 2021