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

Author

Amarnath Murthy, Jan 07 2002

Keywords

• easy
• nonn
• base

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

Examples

			a(4) = floor(2468/1357) = floor(1.81871775976418570375829034635225) = 1.
a(20000) = 18175.
		

References

• Mark I. Krusemeyer, George T. Gilbert, and Loren C. Larson, A Mathematical Orchard, Problems and Solutions, MAA, 2012, Problem 87, pp. 159-161.

Crossrefs

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

Cf. A019519, A019520, A349960.

Programs

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 *)

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

Formula

a(n) = floor(A019520(n)/A019519(n)).

Extensions

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