A028823 - OEIS

%I #41 Sep 08 2022 08:44:50

%S 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,

%T 30,31,35,37,38,40,42,44,45,46,47,49,53,56,57,59,60,62,63,64,70,72,73,

%U 75,76,79,81,82,86,87,91,92,95,98,103,104,108,109,110,113,114

%N Numbers k such that k^2 + k + 17 is prime.

%C Complement of A007636. - _Michel Marcus_, Jun 17 2013

%H Seiichi Manyama, <a href="/A028823/b028823.txt">Table of n, a(n) for n = 1..10000</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>

%e 15^2 + 15 + 17 = 257, which is prime, so 15 is in the sequence.

%e 16^2 + 16 + 17 = 289 = 17^2, so 16 is not in the sequence. Much more obviously, 17 is not in the sequence either.

%t Select[Range[0, 199], PrimeQ[#^2 + # + 17] &] (* _Indranil Ghosh_, Mar 19 2017 *)

%o (Magma) [n: n in [0..1000] |IsPrime(n^2+n+17)] // _Vincenzo Librandi_, Nov 19 2010

%o (PARI) is(n)=isprime(n^2+n+17) \\ _Charles R Greathouse IV_, Feb 20 2017

%o (Python)

%o from sympy import isprime

%o print([n for n in range(201) if isprime(n**2 + n + 17)]) # _Indranil Ghosh_, Mar 19 2017

%Y Cf. A007635, A007636, A014556.

%K nonn

%O 1,3

%A _Patrick De Geest_