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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 (list; graph; refs; listen; history; text; internal format)
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

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Mario Ziller, John F. Morack, Algorithmic concepts for the computation of Jacobsthal's function, arXiv:1611.03310 [math.NT], 2016.

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+i-1], n)>1 do len:=len+1; od:

    if len>rec then rec:=len; fi;

   od:

a:=[op(a), rec];

od:

a; # N. J. A. Sloane, Apr 18 2017

MATHEMATICA

a[ n_ ] := (Max[ Drop[ #, 1 ]-Drop[ #, -1 ] ]-1&)[ Select[ Range[ n+1 ], GCD[ #, n ]==1& ] ]

Do[Print[n, " ", a[n]], {n, 20000}]

CROSSREFS

Equals A048669(n) - 1.

See also A048670, A049298, A070791, A070194.

Sequence in context: A155744 A086869 A095345 * A243915 A309307 A325446

Adjacent sequences:  A132465 A132466 A132467 * A132469 A132470 A132471

KEYWORD

nonn

AUTHOR

Michael Kleber, Nov 16 2007

EXTENSIONS

Incorrect formula removed by Thomas Anton, Dec 30 2018

STATUS

approved

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Last modified September 25 10:05 EDT 2020. Contains 337337 sequences. (Running on oeis4.)