Prime numbers that are not the sum of distinct squares.
2, 3, 7, 11, 19, 23, 31, 43, 47, 67
1
These are the prime numbers at which A033461 is zero.
T. D. Noe, Plot of 10 terms
(Mma) nn = 15; ss = Subsets[Range[nn]^2]; t2 = Select[Tally[Sort[Plus @@@ ss]], #[[1]] <= nn^2 &]; t3 = Complement[Range[nn^2], Transpose[t2][[1]]]; Select[t3, PrimeQ]
Cf. A001422 (prime and composite cases).
nonn,full
T. D. Noe, Mar 23 2016