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A274227
Primes in A274226.
2
29, 53, 61, 109, 157, 277, 397
OFFSET
1,1
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
LINKS
C. Wagner, Class number 5, 6 and 7, Math. Comput. 64 (1996), pp. 785-800.
EXAMPLE
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.
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 *)
CROSSREFS
Sequence in context: A134555 A164075 A117328 * A230027 A105406 A124284
KEYWORD
nonn,fini,full
AUTHOR
Andreas Boe, Jun 14 2016
STATUS
approved