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 A075019 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. 14
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 From Robert Israel, Aug 28 2015: (Start) a(n) = 2 iff n is even. a(n) = 3 iff n == 3 or 5 (mod 6). a(n) = 5 iff n == 25 (mod 30). (End) LINKS Robert Israel and Robert G. Wilson v, Table of n, a(n) for n = 1..462 first 120 terms from Robert Israel. EXAMPLE a(5)= 3, 3 is the smallest prime divisor of 12345. MAPLE with(numtheory): T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end: P:=proc(q) local a, b, n; b:=1; print(1); for n from 2 to q do b:=n+b*10^T(n); a:=sort([op(divisors(b))]); print(a[2]); od; end: P(100); # Paolo P. Lava, Apr 30 2014 # Alternative: C:= 1: A[1]:= 1: for n from 2 to 100 do C:= C*10^(1+ilog10(n))+n; F:= map(t -> t[1], ifactors(C, 'easy')[2]); if hastype(F, integer) then A[n]:= min(select(type, F, integer)) else A[n]:= min(numtheory:-factorset(C)) fi od: seq(A[n], n=1..100); # Robert Israel, Aug 28 2015 MATHEMATICA 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 *) PROG (PARI) lpf(n)=forprime(p=2, 1e3, if(n%p==0, return(p))); factor(n)[1, 1] print1(N=1); for(n=2, 100, N=N*10^#Str(n)+n; print1(", "lpf(N))) \\ Charles R Greathouse IV, Apr 10 2014 CROSSREFS Cf. A000422, A007908, A075020, A104759, A116504, A116505, A138789, A138790, A138958, A138959, A138960, A138961, A138962. Sequence in context: A164962 A251089 A119880 * A138960 A245553 A115397 Adjacent sequences:  A075016 A075017 A075018 * A075020 A075021 A075022 KEYWORD base,nonn AUTHOR Amarnath Murthy, Sep 01 2002 EXTENSIONS More terms from Sascha Kurz, Jan 03 2003 STATUS approved

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