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

0, 4, 6, 8, 9, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24

Offset: 1

Author

Jonathan Vos Post, May 11 2013

Keywords

• nonn
• easy

Comments

Arises in analysis of "when to clean your room".

Examples

			a(3) = floor(4*log_2(3)) = floor(6.33985000) = 6.
a(8) = floor(4*log_2(8)) = floor(4*3) = 12.
		

Links

• Kimball Martin and Krishnan Shankar, How often should you clean your room?, arXiv:1305.1984 [math.CO], 2013-2014.

Crossrefs

Cf. A000583 (n^4), A000523 (floor log_2), A004257 (round log_2), A029837 (ceiling log_2).

Cf. A329202 (log_2(n^2)), A329193 (log_2(n^3)).

Programs

Maple

A225668 := proc(n)
    4*log[2](n) ;
    floor(%) ;
end proc: # R. J. Mathar, May 12 2013

Mathematica

Table[Floor[4*Log[2, n]], {n, 1, 64}] (* Jean-François Alcover, Nov 30 2017 *)

PARI

a(n) = 4*log(n)\log(2); \\ Michel Marcus, Nov 30 2017

PARI

apply( A225668(n)=exponent(n^4), [1..99]) \\ M. F. Hasler, Nov 07 2019

Formula

a(n) = floor(4*log(n)/log(2)).

a(n) = floor(log_2(n^4)) = A000523(A000583(n)), i.e., this A225668 = A000523 o A000583. - M. F. Hasler, Nov 07 2019

Extensions

Better definition from M. F. Hasler, Nov 07 2019