

A007417


If n appears, 3n does not.
(Formerly M0954)


7



1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 36, 37, 38, 40, 41, 43, 44, 45, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 63, 64, 65, 67, 68, 70, 71, 72, 73
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OFFSET

1,2


COMMENTS

The characteristic function of this sequence is given by A014578.  Philippe Deléham, Mar 21 2004
Numbers n such that their ternary representation ends in even number of zeros .  Philippe Deléham, Mar 25 2004
Numbers for which 3 is not infinitary divisor.  Vladimir Shevelev, Mar 18 2013
Where odd terms occur in A051064.  Reinhard Zumkeller, May 23 2013


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n=1..1000
Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012), no. 1, 4246.
David Wakeham and David R. Wood, On multiplicative Sidon sets, INTEGERS, 13 (2013), #A26.


FORMULA

Lim n > infinity a(n)/n = 4/3 .  Philippe Deléham, Mar 21 2004
Partial sums of A092400. Indices of even numbers in A007949. Indices of odd numbers in A051064. a(n) = A092401(2n1).  Philippe Deléham, Mar 29 2004


EXAMPLE

From Gary W. Adamson, Mar 02 2010: (Start)
Given the following multiplication table: top row = "not multiples of 3"
left column = powers of 3; we get:
...
.1...2...4...5...7...8...10...11...13...
.3...6..12..15..21..24...30...33...39...
.9..18..36..45..63..72...90...99..114...
27..54.108..............................
81......................................
... If rows are labeled (1, 2, 3,...) then odd indexed rows are in the set; but
evens not. Examples: 9 is in the set since 3 is not, but 27 in row 4 can't be. (End)


MATHEMATICA

Select[ Range[100], (# // IntegerDigits[#, 3]& // Split // Last // Count[#, 0]& // EvenQ)&] (* JeanFrançois Alcover, Mar 01 2013, after Philippe Deléham *)


PROG

(Haskell)
import Data.List (delete)
a007417 n = a007417_list !! (n1)
a007417_list = s [1..] where
s (x:xs) = x : s (delete (3*x) xs)


CROSSREFS

Complement of A145204. [From Reinhard Zumkeller, Oct 04 2008]
Sequence in context: A039137 A071807 A074232 * A039099 A215069 A035257
Adjacent sequences: A007414 A007415 A007416 * A007418 A007419 A007420


KEYWORD

easy,nonn


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

More terms from Philippe Deléham, Mar 29 2004
Typo corrected by Philippe Deléham, Apr 15 2010


STATUS

approved



