%I #48 Oct 12 2023 07:46:21
%S 0,3,5,6,9,10,12,15,18,20,21,24,25,27,30,33,35,36,39,40,42,45,48,50,
%T 51,54,55,57,60,63,65,66,69,70,72,75,78,80,81,84,85,87,90,93,95,96,99,
%U 100,102,105,108,110,111,114,115,117,120,123,125,126,129,130,132,135
%N Nonnegative numbers k such that k == 0 (mod 3) or k == 0 (mod 5).
%C 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, ...
%C The asymptotic density of this sequence is 7/15. - _Amiram Eldar_, Mar 25 2021
%C For a neat way to supplement the set to achieve equal density with its complement, see A080307. - _Peter Munn_, Oct 12 2023
%H Colin Barker, <a href="/A281746/b281746.txt">Table of n, a(n) for n = 1..1000</a>
%H Rosetta Code, <a href="https://www.rosettacode.org/wiki/FizzBuzz">FizzBuzz</a>.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,1,-1).
%F 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).
%F a(n) = a(n-1) + a(n-7) - a(n-8) for n > 8. - _Colin Barker_, Feb 07 2017
%t 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 *)
%t Union[3Range[0, 33], 5Range[20]] (* _Alonso del Arte_, Sep 03 2018 *)
%t 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 *)
%o (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
%Y Complement of A229829.
%Y Union of A008585 and A008587.
%Y Subset of {0} U A080307.
%K nonn,easy
%O 1,2
%A _Seiichi Manyama_, Jan 29 2017