A287164 Primes having a unique partition into three squares.

2, 3, 5, 11, 13, 19, 37, 43, 67, 163

Offset: 1

Author

Ilya Gutkovskiy, May 20 2017

Keywords

• nonn
• more

Comments

D. H. Lehmer conjectures that there are no more terms (see A094739 and A094942).

Examples

			-------------------------------
|  n | a(n) | representation  |
|-----------------------------|
|  1 |   2  | 0^2 + 1^2 + 1^2 |
|  2 |   3  | 1^2 + 1^2 + 1^2 |
|  3 |   5  | 0^2 + 1^2 + 2^2 |
|  4 |  11  | 1^2 + 1^2 + 3^2 |
|  5 |  13  | 0^2 + 2^2 + 3^2 |
|  6 |  19  | 1^2 + 3^2 + 3^2 |
|  7 |  37  | 0^2 + 1^2 + 6^2 |
|  8 |  43  | 3^2 + 3^2 + 5^2 |
|  9 |  67  | 3^2 + 3^2 + 7^2 |
| 10 | 163  | 1^2 + 9^2 + 9^2 |
-------------------------------
157 is the prime of the form x^2 + y^2 + z^2 with x, y, z >= 0, but is not in the sequence because 157 = 0^2 + 6^2 + 11^2 = 2^2 + 3^2 + 12^2.
		

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000164, A000378, A002313, A042998, A094739, A094942.

Programs

Mathematica

Select[Range[200], Length[PowersRepresentations[#, 3, 2]] == 1 && PrimeQ[#] &]