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 A266651 #15 Jan 06 2016 06:27:19
%S A266651 14,21,62,190,206,210,237,286,334,350,382,398,426,430,446,453,574,622,
%T A266651 670,734,766,777,782,878,958,974,1102,1294,1317,1342,1438,1486,1678,
%U A266651 1694,1722,1749,1774,1790,1938,1965,1966,2014,2030,2110,2126,2154,2222,2254,2270,2289,2302,2397,2414,2446,2558,2638,2686,2721,2734,2750
%N A266651 Nonnegative integers x such that x^3 + 6^3 is a sum of two squares.
%C A266651 Conjecture: For any integer x with gcd(x,6) = 1, the number x^3 + 6^3 is never a sum of two squares.
%C A266651 We have verified this for x up to 5*10^6.
%C A266651 Note also that 6^3 + (-2)^3 = 8^2 + 12^2.
%C A266651 Hao Pan at Nanjing Univ. confirmed the conjecture on Jan. 3, 2016. - _Zhi-Wei Sun_, Jan 06 2016
%H A266651 Zhi-Wei Sun, <a href="/A266651/b266651.txt">Table of n, a(n) for n = 1..10000</a>
%e A266651 a(1) = 14 since 14^3 + 6^3 = 16^2 + 52^2.
%e A266651 a(7) = 237 since 237^3 + 6^3 = 162^2 + 3645^2.
%t A266651 f[n_]:=f[n]=FactorInteger[n]
%t A266651 Le[n_]:=Le[n]=Length[f[n]]
%t A266651 n=0;Do[Do[If[Mod[Part[Part[f[x^3+6^3],i],1],4]==3&&Mod[Part[Part[f[x^3+6^3],i],2],2]==1,Goto[aa]],{i,1,Le[216+x^3]}];n=n+1;Print[n," ",x];Label[aa];Continue,{x,0,2750}]
%Y A266651 Cf. A000290, A000578, A001481, A266152, A266230, A266231, A266277, A266363, A266364, A266548.
%K A266651 nonn
%O A266651 1,1
%A A266651 _Zhi-Wei Sun_, Jan 02 2016