A339988 Prime numbers that are the sum of an odd square s and an even square t such that 0 < s < t.

5, 17, 37, 61, 73, 89, 101, 109, 113, 149, 181, 193, 197, 257, 277, 281, 317, 337, 349, 373, 401, 409, 449, 509, 521, 569, 577, 601, 613, 653, 677, 701, 709, 757, 761, 773, 797, 809, 937, 953, 1009, 1021, 1033, 1049, 1069, 1117, 1181, 1193, 1237, 1249, 1277, 1297, 1301

Offset

1,1

Links

Table of n, a(n) for n=1..53.

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

Cf. A010051, A010052.

Sequence in context: A119456 A264904 A257582 * A273538 A273212 A273274

Adjacent sequences: A339985 A339986 A339987 * A339989 A339990 A339991

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 25 2020

Status

approved