cp's OEIS Frontend

A268307 Integers n such that A005897(n) is the sum of two positive cubes.

%I A268307 #12 Mar 07 2016 12:48:32
%S A268307 5,11,17,28,37,81,87,107,141,178,200,205,229,296,301,377,385,395,427,
%T A268307 497,511,595,613,641,660,907,914,921,955,975,983,991,1043,1129,1265,
%U A268307 1343,1369,1382,1409,1537,1552,1601,1819,1838,1839,1917,1922,1979,2205,2299,2381,2581,2649,2663
%N A268307 Integers n such that A005897(n) is the sum of two positive cubes.
%C A268307 The number of unit cubes on the surface of an n X n X n cube is given by sequence A005897.
%C A268307 With a pair of scales, one might incorrectly think a single cube could be equal to the sum of two cubes. However, we know this is impossible because of Fermat's Last Theorem.
%C A268307 But we can put a 6 X 6 X 6 cube containing only surface unit cubes on one scale: there are 152 unit cubes. In other side of the scale we can put a 3 X 3 X 3 cube and a 5 X 5 X 5 cube, so there are 27 unit cubes and 125 unit cubes, and the two pans balance.
%e A268307 5 is a term because A005897(5) = 152 = 3^3 + 5^3.
%e A268307 11 is a term because A005897(11) = 728 = 6^3 + 8^3.
%e A268307 17 is a term because A005897(17) = 1736 = 2^3 + 12^3.
%t A268307 Select[Range@ 2700, Length[PowersRepresentations[6 #^2 + 2, 2, 3] /. {0, _} -> Nothing] > 0 &] (* _Michael De Vlieger_, Feb 01 2016 *)
%o A268307 (PARI) T = thueinit('z^3+1);
%o A268307 is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
%o A268307 a(n) = if(n, 6*n^2+2, 1);
%o A268307 for(n=0, 1e4, if(is(a(n)), print1(n, ", ")));
%Y A268307 Cf. A003325, A005897.
%K A268307 nonn,easy
%O A268307 1,1
%A A268307 _Altug Alkan_, Jan 31 2016