A339989 Primes that are the sum of an even square s and an odd square t such that 0 < s < t.

13, 29, 41, 53, 97, 137, 157, 173, 229, 233, 241, 269, 293, 313, 353, 389, 397, 421, 433, 457, 461, 541, 557, 593, 617, 641, 661, 673, 733, 769, 821, 829, 853, 857, 877, 881, 929, 941, 977, 997, 1013, 1061, 1093, 1097, 1109, 1129, 1153, 1201, 1213, 1217, 1229, 1289, 1361

Offset

1,1

Links

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

Example

29 is in the sequence since it is a prime such that 2^2 + 5^2 = 4 + 25 = 29, 4 is even, 25 is odd, and 0 < 4 < 25.

Mathematica

Table[If[(PrimePi[n] - PrimePi[n - 1])*Sum[Mod[i + 1, 2] Mod[n - i, 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

Crossrefs

Cf. A010051, A010052.

Sequence in context: A141293 A339956 A352926 * A120827 A369863 A320631

Adjacent sequences: A339986 A339987 A339988 * A339990 A339991 A339992

Keyword

nonn

Author

Wesley Ivan Hurt, Dec 25 2020

Status

approved