

A022552


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


21



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
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OFFSET

1,1


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. ZhiWei 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, PatternAvoiding Permutations [Broken link?]
Steven Finch, PatternAvoiding Permutations [Cached copy, with permission]
W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169173.
ZhiWei 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


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], #]& (* JeanFrançois Alcover, Mar 23 2020 *)


CROSSREFS

Complement of A022551.
Sequence in context: A053354 A346197 A274700 * A082658 A022389 A041225
Adjacent sequences: A022549 A022550 A022551 * A022553 A022554 A022555


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Will Jagy


STATUS

approved



