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A081290
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a(0) = 0, and for n >=1, a(n) = the largest Catalan number <= n.
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11
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0, 1, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42
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OFFSET
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0,3
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COMMENTS
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For all n>0, a(A000108(n)) = A000108(n) [the first occurrence of the n-th Catalan number in this sequence].
Minimal i such that A081289(i) >= A081289(n) [the original definition of the sequence].
In other words, the first position k in A081289 where A081289(n) occurs (the minimal k such that A081289(k) = A081289(n)), and also the first position k in A081288 where A081288(n) occurs (the minimal k such that A081288(k) = A081288(n)). The starting point of the run which contains the n-th term in those sequences.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n)^2 = 44*Pi/sqrt(3) - 4*Pi^2 - 38. - Amiram Eldar, Aug 18 2022
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MATHEMATICA
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Join[{0}, With[{catnos=Reverse[CatalanNumber[Range[10]]]}, Table[ SelectFirst[ catnos, #<=n&], {n, 80}]]] (* This program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Jul 27 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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