

A132468


Longest gap between numbers relatively prime to n.


4



0, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 2, 1, 1, 3, 1, 3, 2, 3, 1, 3, 1, 3, 1, 3, 1, 5, 1, 1, 2, 3, 2, 3, 1, 3, 2, 3, 1, 5, 1, 3, 2, 3, 1, 3, 1, 3, 2, 3, 1, 3, 2, 3, 2, 3, 1, 5, 1, 3, 2, 1, 2, 5, 1, 3, 2, 5, 1, 3, 1, 3, 2, 3, 2, 5, 1, 3, 1, 3, 1, 5, 2, 3, 2, 3, 1, 5, 2, 3, 2, 3, 2, 3, 1, 3, 2, 3, 1, 5, 1, 3, 4
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OFFSET

1,6


COMMENTS

Here "gap" does not include the endpoints.
a(n) is given by the maximum length of a run of numbers satisfying one congruence modulo each of n's distinct prime factors. It follows that if m is the number of distinct prime factors of n and each of n's prime factors is greater than m then a(n) = m.  Thomas Anton, Dec 30 2018


LINKS



FORMULA

a(n) = 1 at every prime power.


EXAMPLE

E.g. n=3: the longest gap in 1, 2, 4, 5, 7, ... is 1, between 2 and 4, so a(3) = 1.


MAPLE

a:=[];
for n from 1 to 120 do
s:=[seq(j, j=1..4*n)];
rec:=0;
for st from 1 to n do
len:=0;
for i from 1 to n while gcd(s[st+i1], n)>1 do len:=len+1; od:
if len>rec then rec:=len; fi;
od:
a:=[op(a), rec];
od:


MATHEMATICA

a[ n_ ] := (Max[ Drop[ #, 1 ]Drop[ #, 1 ] ]1&)[ Select[ Range[ n+1 ], GCD[ #, n ]==1& ] ]
Do[Print[n, " ", a[n]], {n, 20000}]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



