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Floor[X/Y] where X = concatenation in increasing order of first n powers of 2 and Y = that of first n natural numbers.
6

%I #7 Dec 30 2018 16:18:11

%S 2,2,2,20,201,2010,201012,20101226,2010122457,201012245610,

%T 20101224560848,2010122456084687,201012245608468521,

%U 201012245608468519453,201012245608468519428723,201012245608468519428463029,2010122456084685194284602619644

%N Floor[X/Y] where X = concatenation in increasing order of first n powers of 2 and Y = that of first n natural numbers.

%e a(6)= floor [ 248163264/123456] = floor[2010.13530326594090202177293] = 2010.

%t f[n_] := (k = 1; x = y = "0"; While[k < n + 1, x = StringJoin[x, ToString[2^k]]; y = StringJoin[y, ToString[k]]; k++ ]; Return[ Floor[ ToExpression[x] / ToExpression[y]]] ); Table[ f[n], {n, 1, 20} ]

%t Table[Floor[FromDigits[Flatten[IntegerDigits/@(2^Range[n])]]/FromDigits[ Flatten[IntegerDigits/@Range[n]]]],{n,20}] (* _Harvey P. Dale_, Dec 30 2018 *)

%Y Cf. A067088, A067089, A067090, A067091, A067092, A067093, A067094, A067095, A067096.

%Y floor[A045507(n)/A019519(n)]

%K easy,base,nonn

%O 1,1

%A _Amarnath Murthy_, Jan 07 2002

%E More terms from _Robert G. Wilson v_, Jan 09 2002

%E More terms from _Harvey P. Dale_, Dec 30 2018