%I #51 Dec 31 2023 10:12:28

%S 1,2,3,2,3,2,127,2,3,2,3,2,113,2,3,2,3,2,13,2,3,2,3,2,5,2,3,2,3,2,29,

%T 2,3,2,3,2,71,2,3,2,3,2,7,2,3,2,3,2,23,2,3,2,3,2,5,2,3,2,3,2,10386763,

%U 2,3,2,3,2,397,2,3,2,3,2,37907,2,3,2,3,2,73,2,3,2,3,2,5,2,3,2,3,2,37,2,3,2

%N a(1) = 1; for n > 1, a(n) = the smallest prime divisor of the number C(n) formed from the concatenation of 1,2,3,... up to n.

%C Least prime factor of A007908(n). For 1 < n <= 5000, a(n) < A007908(n), but this should fail infinitely often (assuming standard heuristics). - _Charles R Greathouse IV_, Apr 10 2014

%C From _Robert Israel_, Aug 28 2015: (Start)

%C a(n) = 2 iff n is even.

%C a(n) = 3 iff n == 3 or 5 (mod 6).

%C a(n) = 5 iff n == 25 (mod 30). (End)

%H Robert G. Wilson v, <a href="/A075019/b075019.txt">Table of n, a(n) for n = 1..1000</a> (first 120 terms from Robert Israel)

%e a(5)= 3, 3 is the smallest prime divisor of 12345.

%p C:= 1: A[1]:= 1:

%p for n from 2 to 100 do

%p C:= C*10^(1+ilog10(n))+n;

%p F:= map(t -> t[1],ifactors(C,'easy')[2]);

%p if hastype(F,integer) then A[n]:= min(select(type,F,integer))

%p else A[n]:= min(numtheory:-factorset(C))

%p fi

%p od:

%p seq(A[n],n=1..100); # _Robert Israel_, Aug 28 2015

%t a = {}; b = {}; Do[w = RealDigits[n]; w = First[w]; Do[AppendTo[a, w[[k]]], {k, Length[w]}]; p = FromDigits[a]; AppendTo[b,First[First[FactorInteger[ p]]]], {n, 25}]; b (* _Artur Jasinski_, Apr 04 2008 *)

%o (PARI) lpf(n)=forprime(p=2,1e3,if(n%p==0,return(p))); factor(n)[1,1]

%o print1(N=1);for(n=2,100,N=N*10^#Str(n)+n; print1(", "lpf(N))) \\ _Charles R Greathouse IV_, Apr 10 2014

%Y Cf. A000422, A007908, A075020, A104759, A116504, A116505, A138789, A138790, A138960, A138961, A138962.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Sep 01 2002

%E More terms from _Sascha Kurz_, Jan 03 2003