A287164 Primes having a unique partition into three squares.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..10.

Index entries for sequences related to sums of squares

Example

-------------------------------
|  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.

Mathematica

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

Crossrefs

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

Sequence in context: A224321 A053184 A228445 * A020607 A358719 A235631

Adjacent sequences: A287161 A287162 A287163 * A287165 A287166 A287167

Keyword

nonn,more

Author

Ilya Gutkovskiy, May 20 2017

Status

approved