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A225668 a(n) = floor(4*log_2(n)).

%I A225668 #36 Nov 02 2024 06:49:46
%S A225668 0,4,6,8,9,10,11,12,12,13,13,14,14,15,15,16,16,16,16,17,17,17,18,18,
%T A225668 18,18,19,19,19,19,19,20,20,20,20,20,20,20,21,21,21,21,21,21,21,22,22,
%U A225668 22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,24
%N A225668 a(n) = floor(4*log_2(n)).
%C A225668 Arises in analysis of "when to clean your room".
%H A225668 Kimball Martin and Krishnan Shankar, <a href="http://arxiv.org/abs/1305.1984">How often should you clean your room?</a>, arXiv:1305.1984 [math.CO], 2013-2014.
%F A225668 a(n) = floor(4*log(n)/log(2)).
%F A225668 a(n) = floor(log_2(n^4)) = A000523(A000583(n)), i.e., this A225668 = A000523 o A000583. - _M. F. Hasler_, Nov 07 2019
%e A225668 a(3) = floor(4*log_2(3)) = floor(6.33985000) = 6.
%e A225668 a(8) = floor(4*log_2(8)) = floor(4*3) = 12.
%p A225668 A225668 := proc(n)
%p A225668     4*log[2](n) ;
%p A225668     floor(%) ;
%p A225668 end proc: # _R. J. Mathar_, May 12 2013
%t A225668 Table[Floor[4*Log[2, n]], {n, 1, 64}] (* _Jean-François Alcover_, Nov 30 2017 *)
%o A225668 (PARI) a(n) = 4*log(n)\log(2); \\ _Michel Marcus_, Nov 30 2017
%o A225668 (PARI) apply( A225668(n)=exponent(n^4), [1..99]) \\ _M. F. Hasler_, Nov 07 2019
%Y A225668 Cf. A000583 (n^4), A000523 (floor log_2), A004257 (round log_2), A029837 (ceiling log_2).
%Y A225668 Cf. A329202 (log_2(n^2)), A329193 (log_2(n^3)).
%K A225668 nonn,easy
%O A225668 1,2
%A A225668 _Jonathan Vos Post_, May 11 2013
%E A225668 Better definition from _M. F. Hasler_, Nov 07 2019