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

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

Offset: 1

Author

Zak Seidov, Mar 20 2012

Keywords

• nonn

Comments

Note that there are no primes = 7 mod 8.

This sequence is probably complete. Is there a proof?

There are no more terms < 10^7. - Donovan Johnson, Mar 22 2012

Examples

			{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}.
		

Crossrefs

Cf. A181786, A210338.