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A082082 Number of steps to reach 1 in the process of expanding the interval (i1,i2) successively to right and left, such that i1 and i2 always stay coprime, starting with (n,n). 1

%I

%S 1,1,3,1,3,5,4,5,7,4,9,7,9,9,10,9,7,10,13,13,14,10,14,15,17,18,19,16,

%T 18,21,16,17,22,17,23,20,24,23,22,24,27,24,28,28,26,28,28,30,28,33,34,

%U 27,35,35,36,36,35,32,32,38,35,39,43,38,44,41,36,45,45

%N Number of steps to reach 1 in the process of expanding the interval (i1,i2) successively to right and left, such that i1 and i2 always stay coprime, starting with (n,n).

%C In other words: start with (i1=n,i2=n), go up from i2 to the next number coprime to i1. Let this be the new i2. Then go down from i1 to the next number coprime to i2. Let this be the new i1. Then a(n) is the number of these steps needed to reach i1 = 1.

%C Obviously, a(n) < n.

%e Example: (6,6)->(5,7)->(3,8)->(1,10), so a(6) = 3.

%e (7,7)->(5,8)->(4,9)->(3,11)->(2,13)->(1,15), a(7) = 5.

%o (PARI) for(n=2,100,count=0:left=n:right=n:c=n:g=n:f=1:while(g>1,count=count+1:while(gcd(g,c)>1,c=c+f):g=c: if(f<0,left=c:c=right+1,right=c:c=left-1):f=-f):print1(count/2","))

%Y Cf. A084425.

%K nonn

%O 2,3

%A _Amarnath Murthy_, Jun 02 2003

%E Edited by _Ralf Stephan_, Jun 27 2003

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Last modified February 26 09:39 EST 2020. Contains 332277 sequences. (Running on oeis4.)