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

1,1

Links

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

Formula

Intersection of A001358 and A348897.

Example

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

Prog

(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

Crossrefs

Cf. A001358, A348897.

Sequence in context: A341922 A007526 A233536 * A318121 A357785 A369229

Adjacent sequences: A349199 A349200 A349201 * A349203 A349204 A349205

Keyword

nonn

Author

Peter Luschny, Nov 11 2021

Status

approved