# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a075019 Showing 1-1 of 1 %I A075019 #51 Dec 31 2023 10:12:28 %S A075019 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 A075019 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 A075019 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 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. %C A075019 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 A075019 From _Robert Israel_, Aug 28 2015: (Start) %C A075019 a(n) = 2 iff n is even. %C A075019 a(n) = 3 iff n == 3 or 5 (mod 6). %C A075019 a(n) = 5 iff n == 25 (mod 30). (End) %H A075019 Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 120 terms from Robert Israel) %e A075019 a(5)= 3, 3 is the smallest prime divisor of 12345. %p A075019 C:= 1: A[1]:= 1: %p A075019 for n from 2 to 100 do %p A075019 C:= C*10^(1+ilog10(n))+n; %p A075019 F:= map(t -> t[1],ifactors(C,'easy')[2]); %p A075019 if hastype(F,integer) then A[n]:= min(select(type,F,integer)) %p A075019 else A[n]:= min(numtheory:-factorset(C)) %p A075019 fi %p A075019 od: %p A075019 seq(A[n],n=1..100); # _Robert Israel_, Aug 28 2015 %t A075019 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 A075019 (PARI) lpf(n)=forprime(p=2,1e3,if(n%p==0,return(p))); factor(n)[1,1] %o A075019 print1(N=1);for(n=2,100,N=N*10^#Str(n)+n; print1(", "lpf(N))) \\ _Charles R Greathouse IV_, Apr 10 2014 %Y A075019 Cf. A000422, A007908, A075020, A104759, A116504, A116505, A138789, A138790, A138960, A138961, A138962. %K A075019 base,nonn %O A075019 1,2 %A A075019 _Amarnath Murthy_, Sep 01 2002 %E A075019 More terms from _Sascha Kurz_, Jan 03 2003 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE