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%I #30 Sep 08 2022 08:45:13
%S 5,13,5,97,5,13,5,17,5,13,5,97,5,13,5,3041,5,13,5,41,5,13,5,17,5,13,5,
%T 97,5,13,5,1153,5,13,5,97,5,13,5,17,5,13,5,89,5,13,5,193,5,13,5,97,5,
%U 13,5,17,5,13,5,41,5,13,5,769,5,13,5,97,5,13,5,17,5,13,5
%N Smallest prime factor of 2^n+3^n.
%C If n = 4*k+1 or 4*k+3 then 2^n+3^n is divisible by 5.
%C If n = 4*k+2 then 2^n+3^n is divisible by 13.
%C Case n = 4*k including especially n = 2^j cannot be discussed with elementary tools and primality of 2^n+3^n remains open.
%C a(n) = 17 for n == 8 (mod 16). - _Bruno Berselli_, Dec 23 2019
%H Antti Karttunen, <a href="/A094473/b094473.txt">Table of n, a(n) for n = 1..1023</a>
%F a(n) = A020639(A007689(n)). - _Antti Karttunen_, Nov 01 2018
%t mif[x_]:=Part[Flatten[FactorInteger[x]], 1] Table[mif[2^w+3^w], {w, 1, 75}]
%t FactorInteger[#][[1,1]]&/@Table[2^n+3^n,{n,80}] (* _Harvey P. Dale_, Mar 26 2019 *)
%o (PARI) a(n)=factor(2^n+3^n)[1,1] \\ _Charles R Greathouse IV_, Apr 29 2015
%o (PARI) A094473(n) = { my(k=(2^n+3^n)); forprime(p=2,k,if(!(k%p),return(p))); }; \\ _Antti Karttunen_, Nov 01 2018
%o (GAP) List([1..80],n->Factors(2^n+3^n)[1]); # _Muniru A Asiru_, Nov 01 2018
%o (Magma) [Min(PrimeFactors(2^n+3^n)): n in[1..100]]; // _Vincenzo Librandi_, Dec 23 2019
%o (Magma) [PrimeFactors(2^n+3^n)[1]: n in[1..600]]; // _Bruno Berselli_, Dec 23 2019
%Y Cf. A007689, A020639, A050244, A082101, A094474-A094494.
%K nonn
%O 1,1
%A _Labos Elemer_, Jun 02 2004
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