login
Numbers n such that (n^2 + 3)/4 is prime.
4

%I #24 Sep 08 2022 08:45:11

%S 3,5,7,11,13,17,25,29,31,35,41,43,49,55,67,77,83,101,109,115,119,125,

%T 133,139,143,151,155,157,161,179,181,199,203,211,221,223,235,239,263,

%U 277,283,287,295,301,307,311,323,325,329,335,337,347,353,377,379,385

%N Numbers n such that (n^2 + 3)/4 is prime.

%C Under Bunyakovsky's conjecture this sequence is infinite. - _Charles R Greathouse IV_, Dec 28 2011

%H Vincenzo Librandi, <a href="/A088503/b088503.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 2*A002384(n) + 1 = sqrt(A110284(n)). - _Ray Chandler_, Sep 07 2005

%e (25*25 + 3)/4 = 157, 157 is prime, 25 is the 7th term of the sequence.

%t Select[Range[500], PrimeQ[(#^2 + 3)/4] &] (* _Vincenzo Librandi_, Oct 06 2012 *)

%o (PARI) for(k=2,1e3,if(isprime(k^2+k+1),print1(2*k+1", "))) \\ _Charles R Greathouse IV_, Dec 28 2011

%o (Magma) [n: n in [1..400 by 2] | IsPrime((n^2 + 3) div 4)]; // _Vincenzo Librandi_, Oct 06 2012

%Y Cf. A002383, A002384, A110284.

%K easy,nonn

%O 1,1

%A _Pierre CAMI_, Nov 13 2003

%E Corrected and extended by _Ray Chandler_, Nov 16 2003