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A281746
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Nonnegative numbers k such that k == 0 (mod 3) or k == 0 (mod 5).
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1
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0, 3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30, 33, 35, 36, 39, 40, 42, 45, 48, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 78, 80, 81, 84, 85, 87, 90, 93, 95, 96, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 120, 123, 125, 126, 129, 130, 132, 135
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OFFSET
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1,2
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COMMENTS
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In the game "FizzBuzz", players replace any number divisible by three with the word "Fizz", and any number divisible by five with the word "Buzz". But multiples of both three and five are replaced by "FizzBuzz". For example, 1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz, 16, 17, Fizz, 19, Buzz, Fizz, 22, 23, Fizz, Buzz, 26, Fizz, 28, 29, FizzBuzz, ...
The asymptotic density of this sequence is 7/15. - Amiram Eldar, Mar 25 2021
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
Rosetta Code, FizzBuzz.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,1,-1).
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FORMULA
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G.f.: -(3*x^8 + 2*x^7 + x^6 + 3*x^5 + x^4 + 2*x^3 + 3*x^2) / (-x^8 + x^7 + x - 1).
a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. - Colin Barker, Feb 07 2017
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MATHEMATICA
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Select[Range[0, 200], MemberQ[Mod[#, {3, 5}], 0]&] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 3, 5, 6, 9, 10, 12, 15}, 80] (* Harvey P. Dale, Apr 01 2018 *)
Union[3Range[0, 33], 5Range[20]] (* Alonso del Arte, Sep 03 2018 *)
CoefficientList[Series[-(3*x^7 + 2*x^6 + x^5 + 3*x^4 + x^3 + 2*x^2 + 3*x) / (-x^8 + x^7 + x - 1) , {x, 0, 80}], x] (* Stefano Spezia, Sep 16 2018 *)
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PROG
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(PARI) concat(0, Vec(x^2*(3 + 2*x + x^2 + 3*x^3 + x^4 + 2*x^5 + 3*x^6) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^100))) \\ Colin Barker, Feb 07 2017
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CROSSREFS
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Complement of A229829.
Union of A008585 and A008587.
Sequence in context: A075311 A032786 A080309 * A287162 A018900 A126590
Adjacent sequences: A281743 A281744 A281745 * A281747 A281748 A281749
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KEYWORD
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nonn,easy
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AUTHOR
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Seiichi Manyama, Jan 29 2017
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STATUS
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approved
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