A274227 Primes in A274226.

29, 53, 61, 109, 157, 277, 397

Offset: 1

Author

Andreas Boe, Jun 14 2016

Keywords

• nonn
• fini
• full

Comments

If a(8) exists it must be larger than 10^8.

From a proof outline of Wagner, the discriminants of Q(sqrt(-p)) with class number 6 end at -1588, ending this sequence at 397. - Travis Scott, Feb 09 2023

Examples

			29 is a term because 2^2 + 3^2 + 4^2 = 29 is the only representation of 29 as a sum of 3 positive squares, and those squares are distinct.
41 is not a term because, even though it can be represented in just one way as a sum of 3 distinct squares (1^2 + 2^2 + 6^2) it can also be represented as 3^2 + 4^2 + 4^2.
		

Links

• Andreas Boe, List of values with values of x, y and z attached
• C. Wagner, Class number 5, 6 and 7, Math. Comput. 64 (1996), pp. 785-800.

Crossrefs

Cf. A274226, A025339.

Programs

Mathematica

rp[n_] := Flatten@ IntegerPartitions[n, {3}, Range[Sqrt@n]^2]; Select[
Range[265] // Prime, Length[u = rp[#]] == 3 && Union[u] == Sort[u] &] (* Giovanni Resta, Jun 16 2016 *)
Select[Prime@Range@78,Sum[(-1)^Boole@Xor[Mod[t,4]==1,PowerMod[t,(#-1)/2,#]==1],{t,1,#-1,2}]==6&] (* Travis Scott, Feb 09 2023 *)