A385821 Numbers k such that ceiling((k^2 + 1)/2) is prime.

2, 3, 5, 6, 9, 11, 12, 15, 18, 19, 25, 29, 35, 39, 42, 45, 48, 49, 51, 54, 59, 60, 61, 65, 66, 69, 71, 72, 79, 84, 85, 90, 95, 101, 121, 131, 132, 139, 141, 144, 145, 150, 159, 165, 169, 171, 174, 175, 181, 186, 192, 195, 198, 199, 201, 204, 205, 209, 210, 219, 221, 231, 245, 246

Offset: 1

Author

Emirhan Üçok, Jul 09 2025

Keywords

• nonn
• easy

Examples

			5 is a term since ceiling((5^2 + 1)/2) = 13, which is prime.
8 is not a term since ceiling((8^2 + 1)/2) = 33, which is not prime.
		

Links

• James C. McMahon, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of primes in A080827.

Programs

Mathematica

Select[Range[246],PrimeQ[Ceiling[(#^2+1)/2]]&] (* James C. McMahon, Jul 15 2025 *)

PARI

isok(k) = isprime(ceil((k^2+1)/2)); \\ Michel Marcus, Jul 10 2025

Python

from sympy import isprime
def ok(k): return isprime((k*k + 2) // 2)
print([k for k in range(1, 247) if ok(k)])