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.

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

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

Table of n, a(n) for n=1..65.

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

Cf. A067088, A067089, A067090, A067091, A067092, A067093, A067094.

Cf. A019519, A019520, A349960.

Sequence in context: A256688 A372326 A029582 * A070888 A180849 A067101

Adjacent sequences: A067092 A067093 A067094 * A067096 A067097 A067098

Keyword

easy,nonn,base

Author

Amarnath Murthy, Jan 07 2002

Extensions

More terms from Robert G. Wilson v, Jan 09 2002

Status

approved