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.

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

Offset: 1

Author

Amarnath Murthy, Sep 01 2002

Keywords

• base
• nonn

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)

Examples

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

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 120 terms from Robert Israel)

Crossrefs

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

Programs

Maple

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 *)

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

Extensions

More terms from Sascha Kurz, Jan 03 2003