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A067096 Floor[X/Y] where X = concatenation in increasing order of first n even numbers and Y = that of first n natural numbers. 7

%I

%S 2,2,2,2,19,199,1999,19991,199916,199916,199916,199916,199916,199916,

%T 199916,199916,199916,199916,199916,199916,199916,199916,199916,

%U 199916,199916,199916,199916,199916,199916,199916,199916,199916,199916,199916

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

%C Almost all terms appear only once. However, in the first 5000 terms, the term 2 appears 4 times in a row; the term 199916 appears 41 times in a row; the term 19991620000261183803815753482837892477715440187362570807 appears 401 times in a row; and a term with 556 digits (that begins with the same digits as the term that appears 401 times in a row) appears 4001 times in a row. Does this pattern continue? - _Harvey P. Dale_, Jul 04 2012

%e a(10) = floor[ 2468101214161820/12345678910] = floor[199916.20000441271803658143252326] = 199916.

%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, 40} ]

%t ccat[n_,i_]:=FromDigits[Flatten[IntegerDigits/@Range[i,n,i]]]; Table[ Floor[ ccat[2m,2]/ccat[m,1]],{m,40}] (* _Harvey P. Dale_, Jul 04 2012 *)

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

%Y floor[A019520(n)/A019519(n)]

%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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Last modified November 28 20:15 EST 2014. Contains 250399 sequences.