A028823 Numbers k such that k^2 + k + 17 is prime.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 35, 37, 38, 40, 42, 44, 45, 46, 47, 49, 53, 56, 57, 59, 60, 62, 63, 64, 70, 72, 73, 75, 76, 79, 81, 82, 86, 87, 91, 92, 95, 98, 103, 104, 108, 109, 110, 113, 114

Offset: 1

Author

Patrick De Geest

Keywords

• nonn

Comments

Complement of A007636. - Michel Marcus, Jun 17 2013

Examples

			15^2 + 15 + 17 = 257, which is prime, so 15 is in the sequence.
16^2 + 16 + 17 = 289 = 17^2, so 16 is not in the sequence. Much more obviously, 17 is not in the sequence either.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Crossrefs

Cf. A007635, A007636, A014556.

Programs

Magma

[n: n in [0..1000] |IsPrime(n^2+n+17)] // Vincenzo Librandi, Nov 19 2010

Mathematica

Select[Range[0, 199], PrimeQ[#^2 + # + 17] &] (* Indranil Ghosh, Mar 19 2017 *)

PARI

is(n)=isprime(n^2+n+17) \\ Charles R Greathouse IV, Feb 20 2017

Python

from sympy import isprime
print([n for n in range(201) if isprime(n**2 + n + 17)]) # Indranil Ghosh, Mar 19 2017