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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
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 (list; graph; refs; listen; history; text; internal format)
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=left-1):f=-f):print1(count/2", "))
CROSSREFS
Cf. A084425.
Sequence in context: A173039 A016471 A324294 * A016646 A345943 A342342
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Jun 02 2003
EXTENSIONS
Edited by Ralf Stephan, Jun 27 2003
STATUS
approved

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Last modified June 20 10:31 EDT 2024. Contains 373516 sequences. (Running on oeis4.)