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

4, 15, 65, 85, 203, 259, 671, 803, 1111, 1157, 1261, 1417, 2533, 2669, 3439, 3667, 3893, 4369, 4579, 5567, 6187, 6371, 8027, 9407, 12209, 12557, 13369, 16151, 16771, 17429, 18383, 18589, 20491, 21257, 21731, 26233, 28453, 29489, 30673, 34973, 36121, 36889

Offset: 1

Author

Peter Luschny, Nov 11 2021

Keywords

• nonn

Examples

			1157 is in this sequence because 1157 = (5 + 8)*(5^2 + 8^2) = 13*89.
		

Links

• Peter Luschny, Table of n, a(n) for n = 1..1200

Crossrefs

Cf. A001358, A348897.

Programs

Julia

# Returns the terms less than or equal to b^3.
using Nemo
function A349202List(b)
    b3 = b^3; R = Int[]
    for n in 1:b
        for k in 0:n
            a = (n + k) * (n^2 + k^2)
            a > b3 && break
            isprime(n+k) && isprime(n^2 + k^2) && push!(R, a)
    end end
sort(R) end
A349202List(34) |> println

Formula

Intersection of A001358 and A348897.