This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275083 #9 Mar 31 2017 01:12:28
%S A275083 120,312,813,2136,2680,3224,4404,5340,6420,10060,11320,11824,14008,
%T A275083 15856,26544,28804,34392,47984
%N A275083 Positive integers congruent to 0 or 1 modulo 4 that cannot be written as x^3 + y^2 + z^2 with x,y,z nonnegative integers.
%C A275083 Conjecture: (i) The sequence has totally 18 terms as listed.
%C A275083 (ii) For each r = 2,3 there are infinitely many positive integers n == r (mod 4) not in the form x^3 + y^2 + z^2 with x,y,z nonnegative integers.
%C A275083 Our computation indicates that the sequence has no other terms below 10^6.
%C A275083 Let d be 2 or 6. Clearly, n-d is congruent to 0 or 1 modulo 4 if n is congruent to 2 or 3 modulo 4. So part (i) of the conjecture essentially implies that for each n = 0,1,2,... either n or n-d can be written as x^3 + y^2 + z^2 with x,y,z nonnegative integers.
%e A275083 a(1) = 120 since all those positive integers congruent to 0 or 1 modulo 4 and smaller than 120 can be written as x^3 + y^2 + z^2 with x,y,z nonnegative integers but 120 (divisible by 4) cannot be written in this way.
%t A275083 SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
%t A275083 n=0;Do[If[Mod[m,4]>1,Goto[aa]];Do[If[SQ[m-x^3-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,1,50000}]
%Y A275083 Cf. A000290, A000578, A022551, A022552, A262813, A262857, A272979, A274274.
%K A275083 nonn
%O A275083 1,1
%A A275083 _Zhi-Wei Sun_, Jul 15 2016