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A067095 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. 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
Values taken by this function are in A349960. - Bernard Schott, Dec 18 2021
REFERENCES
Mark I. Krusemeyer, George T. Gilbert, and Loren C. Larson, A Mathematical Orchard, Problems and Solutions, MAA, 2012, Problem 87, pp. 159-161.
LINKS
FORMULA
a(n) = floor(A019520(n)/A019519(n)).
EXAMPLE
a(4) = floor(2468/1357) = floor(1.81871775976418570375829034635225) = 1.
a(20000) = 18175.
MATHEMATICA
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 *)
PROG
(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
a(n) = ae(n)\ao(n); \\ Michel Marcus, Dec 07 2021
CROSSREFS
Sequence in context: A358722 A256688 A029582 * A070888 A180849 A067101
KEYWORD
easy,nonn,base
AUTHOR
Amarnath Murthy, Jan 07 2002
EXTENSIONS
More terms from Robert G. Wilson v, Jan 09 2002
STATUS
approved

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Last modified March 29 08:13 EDT 2024. Contains 371265 sequences. (Running on oeis4.)