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.

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, 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, 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

Offset

2,5

Comments

Related to the Jacobsthal function A048669.

a(n) depends only on the radical A007947(n).

Links

Rémy Sigrist, Table of n, a(n) for n = 2..20000

Example

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.
If n is a prime (or prime power), a(n)=0.

Maple

acf:=[]; wcf:=[];
for n from 2 to 120 do
s:=[seq(j, j=0..4*n)];
rec:=0;
   for st from 0 to n do
   len:=0;
      for i from 1 to n while gcd(s[st+i], n)>1 do len:=len+1; od:
      if len>rec then rec:=len; w:=st; fi;
   od:
acf:=[op(acf), rec];
wcf:=[op(wcf), w];
od:
acf; # A132468
wcf; # A285182

Crossrefs

Cf. A132468, A048669, A007947.

Sequence in context: A100951 A348616 A348613 * A190608 A011991 A234931

Adjacent sequences: A285179 A285180 A285181 * A285183 A285184 A285185

Keyword

nonn

Author

N. J. A. Sloane, Apr 19 2017

Status

approved