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A007417
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If k appears, 3k does not.
(Formerly M0954)
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14
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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)
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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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.
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FORMULA
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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(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
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EXAMPLE
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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)
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane, Simon Plouffe
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EXTENSIONS
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More terms from Philippe Deléham, Mar 29 2004
Typo corrected by Philippe Deléham, Apr 15 2010
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STATUS
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approved
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