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, 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

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

Table of n, a(n) for n=2..70.

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

Adjacent sequences: A082079 A082080 A082081 * A082083 A082084 A082085

Keyword

nonn

Author

Amarnath Murthy, Jun 02 2003

Extensions

Edited by Ralf Stephan, Jun 27 2003

Status

approved