login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138353 Primes of the form k^2 + 9. 3
13, 73, 109, 409, 1033, 1453, 1609, 2713, 3373, 3853, 4909, 6733, 7753, 9613, 10009, 12109, 12553, 13933, 19609, 20173, 25609, 28909, 35353, 36109, 40009, 40813, 44953, 47533, 48409, 58573, 88813, 94873, 102409, 110233, 122509, 128173, 135433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is easy to show that k mod 12 must be 2,4,8,10 and that since k^2 mod 12 = 4, then p mod 12 = 1. In base 12, the sequence is 11, 61, 91, 2X1, 721, X11, E21, 16X1, 1E51, 2291, 2X11, 3X91, 45X1, 5691, 5961, 7011, 7321, 8091, E421, E811, 129X1, where X is for 10, E is for 11. - Walter Kehowski, May 31 2008

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

MATHEMATICA

Intersection[Table[n^2+9, {n, 0, 10^2}], Prime[Range[9*10^3]]] ...or... For[i=9, i<=9, a={}; Do[If[PrimeQ[n^2+i], AppendTo[a, n^2+i]], {n, 0, 100}]; Print["n^2+", i, ", ", a]; i++ ]

Select[Range[400]^2+9, PrimeQ] (* Harvey P. Dale, Jan 31 2017 *)

PROG

(MAGMA) [ a: n in [0..900] | IsPrime(a) where a is n^2+9] // Vincenzo Librandi, Nov 24 2010

(Haskell)

a138353 n = a138353_list

a138353_list = filter ((== 1) . a010051') $ map (+ 9) a000290_list

-- Reinhard Zumkeller, Mar 12 2012

(PARI) is(n)=isprime(n) && issquare(n-9) \\ Charles R Greathouse IV, Aug 21 2017

CROSSREFS

Subsequence of A185086.

Cf. A010051, A000290, A005473.

Sequence in context: A139849 A139911 A097460 * A097402 A255416 A201788

Adjacent sequences:  A138350 A138351 A138352 * A138354 A138355 A138356

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 07 2008

EXTENSIONS

More terms from Vincenzo Librandi, Apr 28 2010

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 May 24 23:45 EDT 2020. Contains 334581 sequences. (Running on oeis4.)