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Smallest prime dividing the composite near-repdigit number 133...33 consisting of a 1 followed by n 3's, where n=A105427.
1

%I #15 Jan 17 2019 13:44:08

%S 7,31,67,151,23,13,7,157,163,107,17,13,7,89,170809,31,13,7,4363363,

%T 251,42169,43,13,7,641,17,6791,109,13,7,31,29,373,261382937,13,7,

%U 101921,82647847,443,13,7,43,1042402171,71,31,13,7,1601,425519761

%N Smallest prime dividing the composite near-repdigit number 133...33 consisting of a 1 followed by n 3's, where n=A105427.

%H FactorDB, <a href="http://factordb.com/index.php?query=(10%5En-1)%2F3%2B10%5En">Factorizations of (10^n-1)/3+10^n</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/13333.htm">Factorizations of 133...33</a>.

%t Transpose[FactorInteger[#]][[1,1]]&/@DeleteCases[Table[ FromDigits[ PadRight[{1},n,3]],{n,2,60}],_?PrimeQ] (* _Harvey P. Dale_, Dec 10 2011 *)

%o (PARI) for(n=1,100,m=10^n+(10^n-1)/3;if(!isprime(m),print1(factorint(m)[1,1]," "))) (Alekseyev)

%Y Cf. A089018.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Apr 08 2005

%E More terms from _Max Alekseyev_, Apr 11 2005