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 A271876 #20 Apr 18 2016 05:44:51
%S A271876 0,2,3,5,8,11,14,17,20
%N A271876 Numbers n such that 3^n is not of the form x^3 + y^3 + z^3 where x, y, z > 0.
%C A271876 This sequence is finite.
%C A271876 If 3^n = x^3 + y^3 + z^3, then 3^(n+3) = 3^3 * 3^n = 3^3 * (x^3 + y^3 + z^3) = (3*x)^3 + (3*y)^3 + (3*z)^3. So if we can find the integer n such that 3^n, 3^(n+1) and 3^(n+2) are sums of 3 positive cubes, we will exactly know that this sequence must be finite. Obviously, the minimum value of n such that 3^n, 3^(n+1) and 3^(n+2) are sums of 3 positive cubes determines the last term of this sequence. Since we can solve the 3^n = x^3 + y^3 + z^3 for n = 21, 22, 23 as in example section, all terms of this sequence is computed in limited range that is 0 <= n <= 20.
%C A271876 Corresponding 3^n values are 1, 9, 27, 243, 6561, 177147, 4782969, 129140163, 3486784401.
%e A271876 21 is not a term because 3^21 = (3^5)^3 + (6*3^5)^3 + (8*3^5)^3.
%e A271876 22 is not a term because 3^22 = (3^7)^3 + (3^7)^3 + (3^7)^3.
%e A271876 23 is not a term because 3^23 = 1658^3 + 3202^3 + 3843^3.
%t A271876 Select[Range[0, 20], Length[PowersRepresentations[3^#, 3, 3] /. {{0, __} -> Nothing}] == 0 &] (* _Michael De Vlieger_, Apr 16 2016 *)
%Y A271876 Cf. A000244, A003072.
%K A271876 nonn,fini,full
%O A271876 1,2
%A A271876 _Altug Alkan_, Apr 16 2016