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%I #22 Dec 18 2021 23:38:16
%S 2,1,1,1,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
%T 18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,
%U 18,18,181,181,181,181,181,181,181,181,181,181,181,181,181,181,181,181
%N 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.
%C 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
%C Values taken by this function are in A349960. - _Bernard Schott_, Dec 18 2021
%D Mark I. Krusemeyer, George T. Gilbert, and Loren C. Larson, A Mathematical Orchard, Problems and Solutions, MAA, 2012, Problem 87, pp. 159-161.
%F a(n) = floor(A019520(n)/A019519(n)).
%e a(4) = floor(2468/1357) = floor(1.81871775976418570375829034635225) = 1.
%e a(20000) = 18175.
%t 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} ]
%t 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 *)
%o (PARI) ae(n)=my(s=""); for(k=1, n, s=Str(s, 2*k)); eval(s); \\ A019520
%o ao(n)=my(s=""); for(k=1, n, s=Str(s, 2*k-1)); eval(s); \\ A019521
%o a(n) = ae(n)\ao(n); \\ _Michel Marcus_, Dec 07 2021
%Y Cf. A067088, A067089, A067090, A067091, A067092, A067093, A067094.
%Y Cf. A019519, A019520, A349960.
%K easy,nonn,base
%O 1,1
%A _Amarnath Murthy_, Jan 07 2002
%E More terms from _Robert G. Wilson v_, Jan 09 2002
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