A267119 Noncube integers n such that n^2 + 1 is the sum of 2 positive cubes.

995, 1191, 1608, 2049, 3988, 4584, 4818, 6323, 12811, 14642, 14806, 16710, 27400, 27672, 28881, 38501, 39192, 44892, 46401, 46818, 53438, 63455, 64086, 65385, 72800, 81711, 98146, 114729, 126624, 142345, 159013, 161573, 169358, 184644, 186363, 197559, 200024, 203432, 211307

Offset

1,1

Comments

Corresponding values of n^2 + 1 are 990026, 1418482, 2585665, 4198402, 15904145, 21013057, 23213125, ...

Prime terms of this sequence are 6323, 38501, 159013, 161573, ...

Sequence focuses on the noncube values of n in order to eliminate trivial solutions of motivation equation that is n^2 + 1 = x^3 + y^3 where x and y are positive integers.

Union of this sequence and all positive cubes give the integers n such that n^2 + 1 are the sum of 2 positive cubes.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..330

Example

995 is a term because 995^2 + 1 = 990026 = 51^3 + 95^3.
1191 is a term because 1191^2 + 1 = 1418482 = 85^3 + 93^3.
1608 is a term because 1608^2 + 1 = 2585665 = 76^3 + 129^3.

Prog

(PARI) T = thueinit('z^3+1);
is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
for(n=2, 200000, if(is(n^2+1) && ispower(n, 3) == 0, print1(n, ", ")))

Crossrefs

Cf. A002522, A003325.

Sequence in context: A181707 A035857 A028513 * A210315 A182694 A234847

Adjacent sequences: A267116 A267117 A267118 * A267120 A267121 A267122

Keyword

nonn

Author

Altug Alkan, Jan 10 2016

Status

approved