

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



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, 18, 21, 16, 17, 22, 17, 23, 20, 24, 23, 22, 24, 27, 24, 28, 28, 26, 28, 28, 30, 28, 33, 34, 27, 35, 35, 36, 36, 35, 32, 32, 38, 35, 39, 43, 38, 44, 41, 36, 45, 45
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OFFSET

2,3


COMMENTS

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.
Obviously, a(n) < n.


LINKS



EXAMPLE

Example: (6,6)>(5,7)>(3,8)>(1,10), so a(6) = 3.
(7,7)>(5,8)>(4,9)>(3,11)>(2,13)>(1,15), a(7) = 5.


PROG

(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=left1):f=f):print1(count/2", "))


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



