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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: A348953 A095345 A342671 * A353235 A243915 A367482 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 July 22 07:42 EDT 2024. Contains 374481 sequences. (Running on oeis4.)