A078402 Numbers k such that k^2 + 5 is prime.

0, 6, 12, 36, 48, 72, 78, 96, 114, 126, 162, 168, 198, 204, 246, 258, 294, 336, 342, 372, 414, 432, 456, 462, 492, 504, 516, 534, 552, 576, 588, 594, 624, 666, 714, 726, 756, 768, 786, 792, 798, 804, 834, 852, 876, 888, 918, 954, 996

Offset: 1

Author

Cino Hilliard, Dec 26 2002

Keywords

• nonn
• easy

Comments

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.

All terms are divisible by 6. - Zak Seidov, Dec 27 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

For the primes see A056905(n).

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).

Programs

Magma

[n: n in [0..1000]| IsPrime(n^2+5)]; // Vincenzo Librandi, Jul 15 2012

Mathematica

Select[Range[0,1000],PrimeQ[#^2+5]&] (* Vincenzo Librandi, Jul 13 2012 *)

PARI

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

Formula

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

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2011