OFFSET
1,1
EXAMPLE
17 is in the sequence since it is a prime such that 1^2 + 4^2 = 1 + 16 = 17, where 1 is odd, 16 is even, and 0 < 1 < 16.
MATHEMATICA
Table[If[(PrimePi[n] - PrimePi[n - 1])*Sum[Mod[i, 2] Mod[n - i + 1, 2] (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]]), {i, Floor[n/2]}] > 0, n, {}], {n, 1200}] // Flatten
osesQ[p_]:=Module[{s=Select[IntegerPartitions[p, {2}], AllTrue[Sqrt[#], IntegerQ]&]}, OddQ[ Min[s]] && EvenQ[Max[s]]]; Select[Prime[Range[250]], osesQ] (* Harvey P. Dale, Aug 02 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Dec 25 2020
STATUS
approved