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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.
17
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
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Sep 01 2002
EXTENSIONS
More terms from Sascha Kurz, Jan 03 2003
STATUS
approved