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A210311 Primes that can be represented exactly in one way as a^2 + b^2 + c^2, 0 < a <= b <= c. 1

%I

%S 3,11,17,19,29,43,53,61,67,73,97,109,157,163,193,277,397

%N Primes that can be represented exactly in one way as a^2 + b^2 + c^2, 0 < a <= b <= c.

%C Note that there are no primes = 7 mod 8.

%C This sequence is probably complete. Is there a proof?

%C There are no more terms < 10^7. - _Donovan Johnson_, Mar 22 2012

%e {p,a,b,c}: {3,1,1,1}, {11,1,1,3}, {17,2,2,3}, {19,1,3,3}, {29,2,3,4}, {43,3,3,5}, {53,1,4,6}, {61,3,4,6}, {67,3,3,7}, {73,1,6,6}, {97,5,6,6}, {109,3,6,8}, {157,2,3,12}, {163,1,9,9}, {193,6,6,11}, {277,4,6,15}, {397,3,8,18}.

%Y Cf. A181786, A210338.

%K nonn

%O 1,1

%A _Zak Seidov_, Mar 20 2012

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)