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Search: id:A082082
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| A082082 |
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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). |
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+0
2
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| 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; listen)
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OFFSET
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2,3
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COMMENT
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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.
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EXAMPLE
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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.
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PROGRAM
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(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", "))
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CROSSREFS
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Cf. A084425.
Sequence in context: A063198 A122582 A016471 this_sequence A016646 A160552 A006257
Adjacent sequences: A082079 A082080 A082081 this_sequence A082083 A082084 A082085
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 02 2003
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EXTENSIONS
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Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 27 2003
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