login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056905 Primes of the form k^2 + 5. 10
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 (list; graph; refs; listen; history; text; internal format)
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

Vincenzo Librandi, Table of n, a(n) for n = 1..1800

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

Cf. A002496, A056899, A049423, A005473.

Sequence in context: A102265 A262340 A128347 * A105412 A271017 A270674

Adjacent sequences:  A056902 A056903 A056904 * A056906 A056907 A056908

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jul 07 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 19:36 EDT 2019. Contains 324234 sequences. (Running on oeis4.)