A228613 - OEIS

%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