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Numbers k such that k^2 + 5 is prime.
20

%I #33 Dec 11 2023 11:44:15

%S 0,6,12,36,48,72,78,96,114,126,162,168,198,204,246,258,294,336,342,

%T 372,414,432,456,462,492,504,516,534,552,576,588,594,624,666,714,726,

%U 756,768,786,792,798,804,834,852,876,888,918,954,996

%N Numbers k such that k^2 + 5 is prime.

%C The sum of the reciprocals of the primes generated from these indices converges to 0.2332142.. The sum of the reciprocals of these indices cannot be computed.

%C All terms are divisible by 6. - _Zak Seidov_, Dec 27 2014

%H Vincenzo Librandi, <a href="/A078402/b078402.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>

%F a(n) = 6 * A056906(n).

%t Select[Range[0,1000],PrimeQ[#^2+5]&] (* _Vincenzo Librandi_, Jul 13 2012 *)

%o (PARI) for(n=0,10^4,q=n^2+5;if(isprime(q),print1(n,", ")));

%o (Magma) [n: n in [0..1000]| IsPrime(n^2+5)]; // _Vincenzo Librandi_, Jul 15 2012

%Y For the primes see A056905(n).

%Y Other sequences of the type "Numbers k such that k^2 + i is prime": A005574 (i=1), A067201 (i=2), A049422 (i=3), A007591 (i=4), this sequence (i=5), A114269 (i=6), A114270 (i=7), A114271 (i=8), A114272 (i=9), A114273 (i=10), A114274 (i=11), A114275 (i=12).

%K nonn,easy

%O 1,2

%A _Cino Hilliard_, Dec 26 2002

%E Offset corrected by _Arkadiusz Wesolowski_, Aug 09 2011