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A094473
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Smallest prime factor of 2^n+3^n.
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20
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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, 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, 13, 5, 17, 5, 13, 5, 41, 5, 13, 5, 769, 5, 13, 5, 97, 5, 13, 5, 17, 5, 13, 5
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OFFSET
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1,1
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COMMENTS
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If n = 4*k+1 or 4*k+3 then 2^n+3^n is divisible by 5.
If n = 4*k+2 then 2^n+3^n is divisible by 13.
Case n = 4*k including especially n = 2^j cannot be discussed with elementary tools and primality of 2^n+3^n remains open.
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LINKS
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FORMULA
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MATHEMATICA
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mif[x_]:=Part[Flatten[FactorInteger[x]], 1] Table[mif[2^w+3^w], {w, 1, 75}]
FactorInteger[#][[1, 1]]&/@Table[2^n+3^n, {n, 80}] (* Harvey P. Dale, Mar 26 2019 *)
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PROG
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(PARI) A094473(n) = { my(k=(2^n+3^n)); forprime(p=2, k, if(!(k%p), return(p))); }; \\ Antti Karttunen, Nov 01 2018
(GAP) List([1..80], n->Factors(2^n+3^n)[1]); # Muniru A Asiru, Nov 01 2018
(Magma) [Min(PrimeFactors(2^n+3^n)): n in[1..100]]; // Vincenzo Librandi, Dec 23 2019
(Magma) [PrimeFactors(2^n+3^n)[1]: n in[1..600]]; // Bruno Berselli, Dec 23 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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