A022552 Numbers that are not the sum of 2 squares and a nonnegative cube.

7, 15, 22, 23, 39, 55, 70, 71, 78, 87, 94, 103, 111, 115, 119, 120, 139, 167, 211, 254, 263, 267, 279, 286, 302, 311, 312, 331, 335, 342, 391, 403, 435, 454, 455, 470, 475, 499, 518, 559, 590, 595, 598, 622, 643, 659, 691, 695, 715, 727, 771

Offset: 1

Author

N. J. A. Sloane, Will Jagy

Keywords

• nonn

Comments

There are 434 terms < 6 * 10^7 of which the largest is 5042631 ~= 5 * 10^6. Is this sequence finite? - David A. Corneth, Jun 23 2018

No more terms < 10^10. - Mauro Fiorentini, Jan 26 2019

For n = 1..434, a(n) + 2 is a term of A022551. Zhi-Wei Sun conjectures that Any n can be written as x^2 + y^2 + z^3 + 0(or 2). - XU Pingya, Jun 02 2020

Links

• R. J. Mathar, David A. Corneth, Table of n, a(n) for n = 1..434 (First 325 terms from R. J. Mathar, now terms < 6 * 10^7)
• Steven Finch, Pattern-Avoiding Permutations [Broken link?]
• Steven Finch, Pattern-Avoiding Permutations [Cached copy, with permission]
• W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169-173.
• Zhi-Wei Sun, New Conjectures on Representations of Integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), No.2, p. 110.
• Index entries for sequences related to sums of squares

Crossrefs

Complement of A022551.

Programs

Maple

isA022552 := proc(n)
    not isA022551(n) ;
end proc:
n := 1:
for c from 0 do
    if isA022552(c) then
        printf("%d %d\n",n,c);
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Sep 02 2016

Mathematica

max = 10^6;
Table[x^2 + y^2 + z^3, {x, 0, Sqrt[max]}, {y, x, Sqrt[max - x^2]}, {z, 0, (max - x^2 - y^2)^(1/3)}] // Flatten // Union // Select[#, # <= max&]& // Complement[Range[max], #]& (* Jean-François Alcover, Mar 23 2020 *)