Search: id:A138353
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%I A138353
%S A138353 13,73,109,409,1033,1453,1609,2713,3373,3853,4909,6733,7753,9613,10009,
%T A138353 12109,12553,13933,19609,20173,25609
%N A138353 Primes of the form n^2+9.
%C A138353 It is easy to show that n mod 12 must be 2,4,8,10 and that since n^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. Keep in mind that 12 is a canonical base for mathematics 
               in general since any prime greater than 3 is of the form 6k+-1, any 
               prime of the form 4k+1 is a sum of squares while any prime of the 
               form 4k+3 is never a sum of squares and lcm(6,4)=12. - Walter A. 
               Kehowski (wkehowski(AT)cox.net), May 31 2008
%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++ ]
%Y A138353 Sequence in context: A139849 A139911 A097460 this_sequence A097402 A139873 
               A142787
%Y A138353 Adjacent sequences: A138350 A138351 A138352 this_sequence A138354 A138355 
               A138356
%K A138353 nonn
%O A138353 1,1
%A A138353 Vladimir Orlovsky (4vladimir(AT)gmail.com), May 07 2008

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