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%I #59 Jun 11 2020 16:53:59
%S 7,15,22,23,39,55,70,71,78,87,94,103,111,115,119,120,139,167,211,254,
%T 263,267,279,286,302,311,312,331,335,342,391,403,435,454,455,470,475,
%U 499,518,559,590,595,598,622,643,659,691,695,715,727,771
%N Numbers that are not the sum of 2 squares and a nonnegative cube.
%C 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
%C No more terms < 10^10. - _Mauro Fiorentini_, Jan 26 2019
%C 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
%H R. J. Mathar, David A. Corneth, <a href="/A022552/b022552.txt">Table of n, a(n) for n = 1..434</a> (First 325 terms from R. J. Mathar, now terms < 6 * 10^7)
%H Steven Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/csolve/av.pdf">Pattern-Avoiding Permutations</a> [Broken link?]
%H Steven Finch, <a href="/A240885/a240885.pdf">Pattern-Avoiding Permutations</a> [Cached copy, with permission]
%H W. Jagy and I. Kaplansky, <a href="https://projecteuclid.org/euclid.em/1062621075">Sums of Squares, Cubes and Higher Powers</a>, Experimental Mathematics, vol. 4 (1995) pp. 169-173.
%H Zhi-Wei Sun, <a href="https://www.researchgate.net/publication/330618242_NEW_CONJECTURES_ON_REPRESENTATIONS_OF_INTEGERS_I">New Conjectures on Representations of Integers (I)</a>, Nanjing Univ. J. Math. Biquarterly 34(2017), No.2, p. 110.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%p isA022552 := proc(n)
%p not isA022551(n) ;
%p end proc:
%p n := 1:
%p for c from 0 do
%p if isA022552(c) then
%p printf("%d %d\n",n,c);
%p n := n+1 ;
%p end if;
%p end do: # _R. J. Mathar_, Sep 02 2016
%t max = 10^6;
%t 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 *)
%Y Complement of A022551.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _Will Jagy_
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