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A287164
Primes having a unique partition into three squares.
0
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).
EXAMPLE
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| 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 |
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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
KEYWORD
nonn,more
AUTHOR
Ilya Gutkovskiy, May 20 2017
STATUS
approved