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A090038
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A series with subsets: Pell and companion Pell numbers.
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1
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3, 6, 4, 3, 14, 3, 10, 3, 4, 7, 3, 34, 3, 5, 4, 3, 24, 3, 7, 3, 3, 7, 3, 17, 3, 4, 5, 3, 82, 3, 6, 4, 3, 12, 3, 11, 3, 4, 6, 3, 58, 3, 5, 4, 18, 3, 8, 3, 8, 3, 21, 3, 4, 5, 3, 41, 3, 6, 4, 3, 10, 3, 13, 3, 4, 6, 3, 198
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 1. a(Pn) = A002203(n), where Pn = n-th Pell number, (A090038: n>0: 1, 2, 5, 12, 29, 70...) and A002203(n) = companion Pell numbers: (n>0: 2, 6, 14, 34, 82...). Example: a(29) = 82, where 29 = P5 and 82 = A002203(5). 2. Similarly, A002203(n) = Pn. Example: a(34) = 12, where 34 = A002203(4) and 12 = P4. 3. A089961 is generated from the same formula except that k = phi^(-1).
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FORMULA
| a(n) = floor(1/({n*k}*(1 - {n*k}))) - 1; where {x} = fractional part of x.
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EXAMPLE
| a(9) = 4. Take {n*k} with k = .414213...= sqrt(2) - 1. Then {9*.414...} = .727922...with (.727922...)*(1 - .727922...) = .1980515...Invert, taking floor = 5. Finally, subtract 1 = 4.
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CROSSREFS
| Cf. A090038, A002203, A089959, A089960, A089961.
Sequence in context: A140072 A187148 A105559 * A006464 A159354 A196500
Adjacent sequences: A090035 A090036 A090037 * A090039 A090040 A090041
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KEYWORD
| nonn,uned
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 20 2003
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