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A001682
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Numbers n such that 3^n, 3^(n+1) and 3^(n+2) have same number of digits.
(Formerly M5109 N2213)
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3
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0, 21, 42, 65, 86, 109, 130, 151, 174, 195, 218, 239, 262, 283, 304, 327, 348, 371, 392, 415, 436, 457, 480, 501, 524, 545, 568, 589, 610, 633, 654, 677, 698, 721, 742, 763, 786, 807, 830, 851, 874, 895, 916, 939, 960, 983, 1004, 1027, 1048
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Equivalently the fractional part of n*log(3) lies between 0 and 1-2log(3), about .04576; 1-2log(3) is also the density of the sequence. - Kevin Costello Aug 08 2002
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REFERENCES
| Murray Klamkin and Joe Lipman, Problem E1238, Amer. Math. Monthly, 64 (1957), 367.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
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MATHEMATICA
| Select[Range[0, 2000], IntegerLength[3^#] == IntegerLength[3^(#+1)] == IntegerLength[3^(#+2)]&] (* From Jean-François Alcover, Nov 24 2011 *)
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PROG
| (Haskell)
a001682 n = a001682_list !! (n-1)
a001682_list = [k | k <- [0..], let m = 3^k, a055642 m == a055642 (9*m)]
-- Reinhard Zumkeller, Oct 10 2011
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CROSSREFS
| First differences give A151910.
Cf. A055642, A000244.
Sequence in context: A114384 A008603 A086794 * A180963 A078440 A175805
Adjacent sequences: A001679 A001680 A001681 * A001683 A001684 A001685
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KEYWORD
| nonn,base,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. K. Guy and Emeric Deutsch, Mar 09 2005
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