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A285182 L = A132468(n) = A048669(n)-1 is the length of the longest run of consecutive numbers that have a common factor with n; a(n) = smallest k >= 0 which starts such a run.

%I A285182 #16 Jun 06 2017 00:28:19
%S A285182 0,0,0,0,2,0,0,0,4,0,2,0,6,5,0,0,2,0,4,6,10,0,2,0,12,0,6,0,2,0,0,11,
%T A285182 16,14,2,0,18,12,4,0,6,0,10,5,22,0,2,0,4,17,12,0,2,10,6,18,28,0,2,0,
%U A285182 30,6,0,25,8,0,16,23,4,0,2,0,36,5,18,21,12,0,4,0,40,0,6,34,42,29,10,0,2,13,22,30
%N A285182 L = A132468(n) = A048669(n)-1 is the length of the longest run of consecutive numbers that have a common factor with n; a(n) = smallest k >= 0 which starts such a run.
%C A285182 Related to the Jacobsthal function A048669.
%C A285182 a(n) depends only on the radical A007947(n).
%H A285182 Rémy Sigrist, <a href="/A285182/b285182.txt">Table of n, a(n) for n = 2..20000</a>
%e A285182 If n = 6, among the numbers k = 0,1,2,3,4,5,6,7,... there is a run of L = 3 consecutive numbers, 2,3,4, all with gcd(k,6)>1, starting at k=2, so a(6) = 2.
%e A285182 If n is a prime (or prime power), a(n)=0.
%p A285182 acf:=[]; wcf:=[];
%p A285182 for n from 2 to 120 do
%p A285182 s:=[seq(j,j=0..4*n)];
%p A285182 rec:=0;
%p A285182    for st from 0 to n do
%p A285182    len:=0;
%p A285182       for i from 1 to n while gcd(s[st+i],n)>1 do len:=len+1; od:
%p A285182       if len>rec then rec:=len; w:=st; fi;
%p A285182    od:
%p A285182 acf:=[op(acf),rec];
%p A285182 wcf:=[op(wcf),w];
%p A285182 od:
%p A285182 acf; # A132468
%p A285182 wcf; # A285182
%Y A285182 Cf. A132468, A048669, A007947.
%K A285182 nonn
%O A285182 2,5
%A A285182 _N. J. A. Sloane_, Apr 19 2017