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A088177
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a(1)=1, a(2)=1; for n>2, a(n) is the smallest positive integer such that the products a(i)*a(i+1), i=1..n-1, are all distinct.
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2
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1, 1, 2, 2, 3, 1, 5, 2, 4, 3, 3, 5, 4, 4, 6, 3, 7, 1, 11, 2, 7, 4, 8, 5, 5, 6, 6, 7, 5, 9, 3, 11, 4, 12, 5, 10, 7, 7, 8, 8, 9, 6, 11, 5, 13, 1, 17, 2, 13, 3, 17, 4, 13, 6, 14, 7, 9, 9, 10, 8, 11, 7, 13, 8, 12, 9, 11, 10, 10, 12, 11, 11, 13, 9, 14, 8, 16, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A088178 is the sequence of distinct products a(i)a(i+1), i=1,2,3,... and appears to be a permutation of the natural numbers.
It appears that for k>2 the kth occurrence of 1 lies between the first occurrences of primes p(2*k-4) and p(2*k-3). For instance, the 5th occurrence of 1 lies between the first occurrences of 13 and 17, the 6th and 7th primes, respectively. [John W. Layman, Nov 16 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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EXAMPLE
| Given that the sequence begins 1,1,2,2,... then a(5)=3, since either of the choices a(5)=1 or a(5)=2 would lead to a repetition of one of the previous products 1,2,4 of adjacent pairs of terms.
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MATHEMATICA
| t = {1, 1}; Do[AppendTo[t, 1]; While[Length[Union[Most[t]*Rest[t]]] < n - 1, t[[-1]]++], {n, 3, 100}]; t (* T. D. Noe, Nov 16 2011 *)
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CROSSREFS
| Cf. A088178.
Sequence in context: A035207 A071281 A204995 * A028507 A096226 A155980
Adjacent sequences: A088174 A088175 A088176 * A088178 A088179 A088180
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Sep 22 2003
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