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

5, 11, 17, 28, 37, 81, 87, 107, 141, 178, 200, 205, 229, 296, 301, 377, 385, 395, 427, 497, 511, 595, 613, 641, 660, 907, 914, 921, 955, 975, 983, 991, 1043, 1129, 1265, 1343, 1369, 1382, 1409, 1537, 1552, 1601, 1819, 1838, 1839, 1917, 1922, 1979, 2205, 2299, 2381, 2581, 2649, 2663

Offset

1,1

Comments

The number of unit cubes on the surface of an n X n X n cube is given by sequence A005897.

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.

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.

Links

Table of n, a(n) for n=1..54.

Example

5 is a term because A005897(5) = 152 = 3^3 + 5^3.
11 is a term because A005897(11) = 728 = 6^3 + 8^3.
17 is a term because A005897(17) = 1736 = 2^3 + 12^3.

Mathematica

Select[Range@ 2700, Length[PowersRepresentations[6 #^2 + 2, 2, 3] /. {0, _} -> Nothing] > 0 &] (* Michael De Vlieger, Feb 01 2016 *)

Prog

(PARI) T = thueinit('z^3+1);
is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
a(n) = if(n, 6*n^2+2, 1);
for(n=0, 1e4, if(is(a(n)), print1(n, ", ")));

Crossrefs

Cf. A003325, A005897.

Sequence in context: A368874 A089110 A023489 * A108294 A046869 A028388

Adjacent sequences: A268304 A268305 A268306 * A268308 A268309 A268310

Keyword

nonn,easy

Author

Altug Alkan, Jan 31 2016

Status

approved