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%I A138353 #25 Sep 08 2022 08:45:33
%S A138353 13,73,109,409,1033,1453,1609,2713,3373,3853,4909,6733,7753,9613,
%T A138353 10009,12109,12553,13933,19609,20173,25609,28909,35353,36109,40009,
%U A138353 40813,44953,47533,48409,58573,88813,94873,102409,110233,122509,128173,135433
%N A138353 Primes of the form k^2 + 9.
%C A138353 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
%H A138353 Reinhard Zumkeller, <a href="/A138353/b138353.txt">Table of n, a(n) for n = 1..10000</a>
%t A138353 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++ ]
%t A138353 Select[Range[400]^2+9,PrimeQ] (* _Harvey P. Dale_, Jan 31 2017 *)
%o A138353 (Magma) [ a: n in [0..900] | IsPrime(a) where a is n^2+9] // _Vincenzo Librandi_, Nov 24 2010
%o A138353 (Haskell)
%o A138353 a138353 n = a138353_list
%o A138353 a138353_list = filter ((== 1) . a010051') $ map (+ 9) a000290_list
%o A138353 -- _Reinhard Zumkeller_, Mar 12 2012
%o A138353 (PARI) is(n)=isprime(n) && issquare(n-9) \\ _Charles R Greathouse IV_, Aug 21 2017
%Y A138353 Subsequence of A185086.
%Y A138353 Cf. A010051, A000290, A005473.
%K A138353 nonn
%O A138353 1,1
%A A138353 _Vladimir Joseph Stephan Orlovsky_, May 07 2008
%E A138353 More terms from _Vincenzo Librandi_, Apr 28 2010

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