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A190839 a(n) is the greatest prime divisor of 10^(2*n)+10^n+1.

%I A190839 #24 Oct 27 2024 10:56:51
%S A190839 37,37,333667,9901,2906161,333667,10838689,99990001,440334654777631,
%T A190839 2906161,1344628210313298373,999999000001,900900900900990990990991,
%U A190839 10838689,4185502830133110721,9999999900000001,13168164561429877,440334654777631,3931123022305129377976519,39526741
%N A190839 a(n) is the greatest prime divisor of 10^(2*n)+10^n+1.
%C A190839 (10^(2*n)+10^n+1)^3 is palindrome.
%H A190839 Amiram Eldar, <a href="/A190839/b190839.txt">Table of n, a(n) for n = 1..158</a>
%H A190839 factordb, <a href="http://factordb.com/index.php?query=10^%282*n%29%2B10^n%2B1&amp;use=n&amp;n=1&amp;VP=on&amp;VC=on&amp;EV=on&amp;OD=on&amp;PR=on&amp;FF=on&amp;PRP=on&amp;CF=on&amp;U=on&amp;C=on&amp;perpage=200&amp;format=1&amp;sent=Show">10^(2*n)+10^n+1</a>.
%F A190839 a(n) = A006530(A066138(n)). - _R. J. Mathar_, Oct 30 2015
%t A190839 f[n_]:=Max[Transpose[FactorInteger[10^(2n)+10^n+1]][[1]]]; Array[f,20] (* _Harvey P. Dale_, Jun 10 2011 *)
%o A190839 (PARI) u(n)=10^(2*n)+10^n+1; for(n=1,30,f=factor(u(n));print1(f[matsize(f)[1],1],", ")) \\ _Joerg Arndt_, May 27 2011
%Y A190839 Cf. A002780, A006530, A066138.
%K A190839 nonn,base
%O A190839 1,1
%A A190839 _Vladimir Shevelev_, May 21 2011