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%I #20 Aug 27 2023 15:36:01
%S 3,29,53,3,59,97,3,23,7,3,31,19,3,5,51131,3,5,2003,3,229,139,3,
%T 4215399123059,5,3,179,5,3,43,7,3,103993,61141,3,19961719,13,3,
%U 2391083871204802979,331,3,89,30707,3,5,601,3,5
%N Least prime factor of (2n+1)^(2n+1)+2
%C Suggested by S. Sykora in a discussion in the OEIS users group on LinkedIn, since the numbers to be factored here are more "elementary" than those of the existing A216146, in turn motivated by A160360.
%C As of today, a(47) seems not yet known.
%H Factor DB, <a href="http://factordb.com/index.php?query=(2*n%2B1)^(2*n%2B1)%2B2">(2*n+1)^(2*n+1)+2</a>.
%F a(3k)=3 for all k >= 0.
%t Table[FactorInteger [((2 n + 1)^(2 n + 1) + 2)][[1, 1]], {n, 0, 46}] (* _Vincenzo Librandi_, Feb 24 2014 *)
%t FactorInteger[#^#+2][[1,1]]&/@Range[1,91,2] (* _Harvey P. Dale_, Aug 27 2023 *)
%o (PARI) A228613=n->factor((2*n+1)^(2*n+1)+2)[1,1]
%Y Cf. A216146, A160360.
%K nonn
%O 0,1
%A _M. F. Hasler_ and _Stanislav Sykora_, Feb 22 2014
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