A299505 Numbers of the form x^4 + y*x^3 + y^2*x^2 + y^3*x + y^4, where x and y are positive integers.

5, 31, 80, 121, 211, 341, 405, 496, 781, 1031, 1280, 1441, 1555, 1936, 2101, 2511, 2801, 3125, 3355, 3376, 4141, 4651, 4681, 5261, 5456, 6480, 6505, 6841, 7381, 7936, 8431, 9031, 9801, 9881, 11111, 11605, 12005, 12496, 13981, 14251, 15961, 16105, 16496, 17091, 17891

Offset: 1

Author

Peter Luschny, Mar 02 2018

Keywords

• nonn

Crossrefs

Cf. A024614, A002649 (subsequence of primes).

Programs

Julia

function isA299505(n)
    n % 5 >= 2 && return false
    n == 5 && return true
    K = Int(floor(5.383*log(n)^1.161))
    M = Int(floor(2*sqrt(n/3)))
    for k in 3:K
        for y in 2:M, x in 1:y
            n == x^4+y*x^3+y^2*x^2+y^3*x+y^4 && return true
    end end
    return false
end
A299505list(upto) = [n for n in 1:upto if isA299505(n)]
println(A299505list(18000))