cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A287164 Primes having a unique partition into three squares.

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%I A287164 #4 May 20 2017 21:49:10
%S A287164 2,3,5,11,13,19,37,43,67,163
%N A287164 Primes having a unique partition into three squares.
%C A287164 D. H. Lehmer conjectures that there are no more terms (see A094739 and A094942).
%H A287164 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A287164 -------------------------------
%e A287164 |  n | a(n) | representation  |
%e A287164 |-----------------------------|
%e A287164 |  1 |   2  | 0^2 + 1^2 + 1^2 |
%e A287164 |  2 |   3  | 1^2 + 1^2 + 1^2 |
%e A287164 |  3 |   5  | 0^2 + 1^2 + 2^2 |
%e A287164 |  4 |  11  | 1^2 + 1^2 + 3^2 |
%e A287164 |  5 |  13  | 0^2 + 2^2 + 3^2 |
%e A287164 |  6 |  19  | 1^2 + 3^2 + 3^2 |
%e A287164 |  7 |  37  | 0^2 + 1^2 + 6^2 |
%e A287164 |  8 |  43  | 3^2 + 3^2 + 5^2 |
%e A287164 |  9 |  67  | 3^2 + 3^2 + 7^2 |
%e A287164 | 10 | 163  | 1^2 + 9^2 + 9^2 |
%e A287164 -------------------------------
%e A287164 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.
%t A287164 Select[Range[200], Length[PowersRepresentations[#, 3, 2]] == 1 && PrimeQ[#] &]
%Y A287164 Cf. A000164, A000378, A002313, A042998, A094739, A094942.
%K A287164 nonn,more
%O A287164 1,1
%A A287164 _Ilya Gutkovskiy_, May 20 2017