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

1,2

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

Example

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

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 *)

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, A138960, A138961, A138962.

Sequence in context: A164962 A251089 A119880 * A138960 A245553 A370455

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