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A067095
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a(n) = floor(X/Y) where X is the concatenation in increasing order of the first n even numbers and Y is that of the first n odd numbers.
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11
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2, 1, 1, 1, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181, 181
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OFFSET
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1,1
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COMMENTS
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For n > 1, the sequence is increasing and tends to infinity. Proof: for k>=1, when the last concatenated integer at the numerator A019520(n) has k digits, then a(n) > 10^(k-1) (see Krusemeyer reference). - Bernard Schott, Dec 06 2021
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REFERENCES
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Mark I. Krusemeyer, George T. Gilbert, and Loren C. Larson, A Mathematical Orchard, Problems and Solutions, MAA, 2012, Problem 87, pp. 159-161.
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LINKS
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FORMULA
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EXAMPLE
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a(4) = floor(2468/1357) = floor(1.81871775976418570375829034635225) = 1.
a(20000) = 18175.
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MATHEMATICA
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f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[2k]]; y = StringJoin[y, ToString[2k - 1]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 75} ]
With[{ev=Range[2, 140, 2], od=Range[1, 139, 2]}, Table[Floor[FromDigits[ Flatten[ IntegerDigits/@ Take[ev, n]]]/FromDigits[Flatten[ IntegerDigits/@ Take[od, n]]]], {n, 70}]] (* Harvey P. Dale, Aug 19 2011 *)
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PROG
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(PARI) ae(n)=my(s=""); for(k=1, n, s=Str(s, 2*k)); eval(s); \\ A019520
ao(n)=my(s=""); for(k=1, n, s=Str(s, 2*k-1)); eval(s); \\ A019521
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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