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

1,2

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

Formula

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

Mathematica

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

Prog

(PARI) for(n=0, 10^4, q=n^2+5; if(isprime(q), print1(n, ", ")));
(Magma) [n: n in [0..1000]| IsPrime(n^2+5)]; // Vincenzo Librandi, Jul 15 2012

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).

Sequence in context: A192029 A166636 A167338 * A127845 A306899 A096932

Adjacent sequences: A078399 A078400 A078401 * A078403 A078404 A078405

Keyword

nonn,easy

Author

Cino Hilliard, Dec 26 2002

Extensions

Offset corrected by Arkadiusz Wesolowski, Aug 09 2011

Status

approved