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Primes in A274226.
2

%I #26 Feb 14 2023 11:22:58

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

%N Primes in A274226.

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

%C 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

%H Andreas Boe, <a href="/A274227/a274227.txt">List of values with values of x, y and z attached</a>

%H C. Wagner, <a href="https://doi.org/10.1090/S0025-5718-96-00722-3">Class number 5, 6 and 7</a>, Math. Comput. 64 (1996), pp. 785-800.

%e 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.

%e 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.

%t rp[n_] := Flatten@ IntegerPartitions[n, {3}, Range[Sqrt@n]^2]; Select[

%t Range[265] // Prime, Length[u = rp[#]] == 3 && Union[u] == Sort[u] &] (* _Giovanni Resta_, Jun 16 2016 *)

%t 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 *)

%Y Cf. A274226, A025339.

%K nonn,fini,full

%O 1,1

%A _Andreas Boe_, Jun 14 2016