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A056905
Primes of the form k^2 + 5.
9
5, 41, 149, 1301, 2309, 5189, 6089, 9221, 13001, 15881, 26249, 28229, 39209, 41621, 60521, 66569, 86441, 112901, 116969, 138389, 171401, 186629, 207941, 213449, 242069, 254021, 266261, 285161, 304709, 331781, 345749, 352841, 389381, 443561
OFFSET
1,1
COMMENTS
Except for a(0), a(n) mod 180 = 41 or 149 since k must be a multiple of 6 without being a multiple of 30 for k^2+5 to be prime.
LINKS
Eric Weisstein's World of Mathematics, Near-Square Prime
FORMULA
a(n) = 36 * A056906(n) + 5.
EXAMPLE
a(2)=149 since 12^2 + 5 = 149, which is prime.
MATHEMATICA
Select[Table[n^2+5, {n, 0, 7000}], PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)
PROG
(Magma) [a: n in [0..700] | IsPrime(a) where a is n^2+5]; // Vincenzo Librandi, Nov 30 2011
(PARI) is(n) = ispseudoprime(n) && issquare(n-5) \\ Felix Fröhlich, May 25 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jul 07 2000
STATUS
approved