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 A007417 If k appears, 3k does not. (Formerly M0954) 18
 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, 74, 76, 77, 79, 80, 81, 82, 83, 85, 86, 88, 89, 90, 91, 92, 94, 95, 97, 98, 99, 100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The characteristic function of this sequence is given by A014578. - Philippe Deléham, Mar 21 2004 Numbers whose ternary representation ends in even number of zeros. - Philippe Deléham, Mar 25 2004 Numbers for which 3 is not an 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 Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe) Aviezri S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math. 312 (2012), no. 1, 42-46. S. Plouffe, Email to N. J. A. Sloane, Jun. 1994 David Wakeham and David R. Wood, On multiplicative Sidon sets, INTEGERS, 13 (2013), #A26. FORMULA Limit_{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(2n-1). - Philippe Deléham, Mar 29 2004 {a(n)} = A052330({A042948(n)}), where {a(n)} denotes the set of integers in the sequence. - Peter Munn, Aug 31 2019 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)&] (* Jean-François Alcover, Mar 01 2013, after Philippe Deléham *) Select[Range[100], EvenQ@ IntegerExponent[#, 3] &] (* Michael De Vlieger, Sep 01 2020 *) PROG (Haskell) import Data.List (delete) a007417 n = a007417_list !! (n-1) a007417_list = s [1..] where    s (x:xs) = x : s (delete (3*x) xs) (PARI) is(n) = { my(i = 0); while(n%3==0, n/=3; i++); i%2==0; } \\ Iain Fox, Nov 17 2017 (PARI) is(n)=valuation(n, 3)%2==0; \\ Joerg Arndt, Aug 08 2020 CROSSREFS Complement of A145204. - Reinhard Zumkeller, Oct 04 2008 Cf. A007949, A014578 (characteristic function), A042948, A051064, A052330, A092400, A092401. Sequence in context: A039137 A071807 A074232 * A039099 A215069 A035257 Adjacent sequences:  A007414 A007415 A007416 * A007418 A007419 A007420 KEYWORD easy,nonn AUTHOR EXTENSIONS More terms from Philippe Deléham, Mar 29 2004 Typo corrected by Philippe Deléham, Apr 15 2010 STATUS approved

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Last modified June 29 07:33 EDT 2022. Contains 354910 sequences. (Running on oeis4.)