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%I #7 Jul 18 2016 23:05:26
%S 15,21,47,53,79,85,92,111,117,120,181,183,245,309,311,335,372,373,398,
%T 405,421,437,447,501,565,573,629,636,645,655,693,757,791,807,820,821,
%U 853,869,885,888,949,967,1013,1045,1077,1141,1205,1223,1269,1271,1303,1461,1555,1591,1613,1653,2087,2101,2255,2421
%N Positive integers not in the form x^3 + 2*y^2 + z^2 with x,y,z nonnegative integers.
%C Conjecture: The sequence has totally 174 terms as listed in the b-file the largest of which is 375565.
%C This implies the conjecture in A275150. We note that the sequence contains no term greater than 375565 and not exceeding 10^6.
%C See also A275168 for a similar conjecture.
%H Zhi-Wei Sun, <a href="/A275169/b275169.txt">Table of n, a(n) for n = 1..174</a>
%e a(1) = 15 since 15 is the least positive integer not in the form x^3 + 2*y^2 + z^2 with x,y,z nonnegative integers.
%t SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
%t n=0;Do[Do[If[SQ[m-x^3-2*y^2],Goto[aa]],{x,0,m^(1/3)},{y,0,Sqrt[(m-x^3)/2]}];n=n+1;Print[n," ",m];Label[aa];Continue,{m,1,2421}]
%Y Cf. A000290, A000578, A022551, A022552, A262813, A270488, A274274, A275083, A275150, A275168.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Jul 18 2016
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