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%I M0954 #85 Jan 15 2022 00:04:53
%S 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,
%T 35,36,37,38,40,41,43,44,45,46,47,49,50,52,53,55,56,58,59,61,62,63,64,
%U 65,67,68,70,71,72,73,74,76,77,79,80,81,82,83,85,86,88,89,90,91,92,94,95,97,98,99,100
%N If k appears, 3k does not.
%C The characteristic function of this sequence is given by A014578. - _Philippe Deléham_, Mar 21 2004
%C Numbers whose ternary representation ends in even number of zeros. - _Philippe Deléham_, Mar 25 2004
%C Numbers for which 3 is not an infinitary divisor. - _Vladimir Shevelev_, Mar 18 2013
%C Where odd terms occur in A051064. - _Reinhard Zumkeller_, May 23 2013
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Iain Fox, <a href="/A007417/b007417.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H Aviezri S. Fraenkel, <a href="http://dx.doi.org/10.1016/j.disc.2011.03.032">The vile, dopey, evil and odious game players</a>, Discrete Math. 312 (2012), no. 1, 42-46.
%H S. Plouffe, <a href="/A007417/a007417.pdf">Email to N. J. A. Sloane, Jun. 1994</a>
%H David Wakeham and David R. Wood, <a href="http://www.emis.de/journals/INTEGERS/papers/n26/n26.Abstract.html">On multiplicative Sidon sets</a>, INTEGERS, 13 (2013), #A26.
%H <a href="/index/Ar#3-automatic">Index entries for 3-automatic sequences</a>.
%F Limit_{n->infinity} a(n)/n = 4/3. - _Philippe Deléham_, Mar 21 2004
%F Partial sums of A092400. Indices of even numbers in A007949. Indices of odd numbers in A051064. a(n) = A092401(2n-1). - _Philippe Deléham_, Mar 29 2004
%F {a(n)} = A052330({A042948(n)}), where {a(n)} denotes the set of integers in the sequence. - _Peter Munn_, Aug 31 2019
%e From _Gary W. Adamson_, Mar 02 2010: (Start)
%e Given the following multiplication table: top row = "not multiples of 3", left column = powers of 3; we get:
%e ...
%e 1 2 4 5 7 8 10 11 13
%e 3 6 12 15 21 24 30 33 39
%e 9 18 36 45 63 72 90 99 114
%e 27 54 108
%e 81
%e ... 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)
%t Select[ Range[100], (# // IntegerDigits[#, 3]& // Split // Last // Count[#, 0]& // EvenQ)&] (* _Jean-François Alcover_, Mar 01 2013, after _Philippe Deléham_ *)
%t Select[Range[100], EvenQ@ IntegerExponent[#, 3] &] (* _Michael De Vlieger_, Sep 01 2020 *)
%o (Haskell)
%o import Data.List (delete)
%o a007417 n = a007417_list !! (n-1)
%o a007417_list = s [1..] where
%o s (x:xs) = x : s (delete (3*x) xs)
%o (PARI) is(n) = { my(i = 0); while(n%3==0, n/=3; i++); i%2==0; } \\ _Iain Fox_, Nov 17 2017
%o (PARI) is(n)=valuation(n,3)%2==0; \\ _Joerg Arndt_, Aug 08 2020
%Y Complement of A145204. - _Reinhard Zumkeller_, Oct 04 2008
%Y Cf. A007949, A014578 (characteristic function), A042948, A051064, A052330, A092400, A092401.
%K easy,nonn
%O 1,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _Philippe Deléham_, Mar 29 2004
%E Typo corrected by _Philippe Deléham_, Apr 15 2010
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