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A078402
Numbers k such that k^2 + 5 is prime.
20
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
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
KEYWORD
nonn,easy,changed
AUTHOR
Cino Hilliard, Dec 26 2002
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Aug 09 2011
STATUS
approved