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A107435
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Triangle T(n,k), 1<=k<=n, read by rows : T(n,k) = length of Euclidean algorithm starting with n and k.
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0
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1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3, 2, 1, 1, 1, 3, 1, 4, 2, 2, 1, 1, 2, 1, 2, 3, 2, 3, 2, 1, 1, 1, 2, 2, 1, 3, 3, 2, 2, 1, 1, 2, 3, 3, 2, 3, 4, 4, 3, 2, 1, 1, 1, 1, 1, 3, 1, 4, 2, 2, 2, 2, 1, 1, 2, 2, 2, 4, 2, 3, 5, 3, 3, 3, 2, 1, 1, 1, 3, 2, 3, 2, 1, 3
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Theorem of Gabriel LAME (1845) : the first value of m in this triangle is T(F(m+2), F(m+1)) where F(n) = A000045(n); example : the first 5 is T(F(7), F(6)) = T(13, 8).
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FORMULA
| T(n, k) = A049816(n, k) + 1.
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EXAMPLE
| 13 = 5*2 + 3, 5 = 3*1 + 2, 3 = 2*1 + 1, 2 = 2*1 + 0 = so that T(13,5) = 4.
Triangle begins:
1
1 1
1 2 1
1 1 2 1
1 2 3 2 1
1 1 1 2 2 1
1 2 2 3 3 2 1
1 1 3 1 4 2 2 1
1 2 1 2 3 2 3 2 1
1 1 2 2 1 3 3 2 2 1
1 2 3 3 2 3 4 4 3 2 1
1 1 1 1 3 1 4 2 2 2 2 1
1 2 2 2 4 2 3 5 3 3 3 2 1
1 1 3 2 3 2 1 3 4 3 4 2 2 1
1 2 1 3 1 2 2 3 3 2 4 2 3 2 1
1 1 2 1 2 3 3 1 4 4 3 2 3 2 2 1
1 2 3 2 3 3 3 2 3 4 4 4 3 4 3 2 1
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CROSSREFS
| Cf. A034883, A049816, A051010.
Sequence in context: A122191 A097847 A144379 * A196056 A161095 A118107
Adjacent sequences: A107432 A107433 A107434 * A107436 A107437 A107438
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 09 2005
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