A138353 Primes of the form k^2 + 9.

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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 07 2008

Keywords

• nonn

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

Crossrefs

Subsequence of A185086.

Cf. A010051, A000290, A005473.

Programs

Haskell

a138353 n = a138353_list
a138353_list = filter ((== 1) . a010051') $ map (+ 9) a000290_list
-- Reinhard Zumkeller, Mar 12 2012

Magma

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

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 *)

PARI

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

Extensions

More terms from Vincenzo Librandi, Apr 28 2010