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A056576 Highest k with 2^k <= 3^n. 14
0, 1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 19, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 38, 39, 41, 42, 44, 45, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 64, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 101, 103, 104, 106, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000

Mike Winkler, The algorithmic structure of the finite stopping time behavior of the 3x+ 1 function, arXiv:1709.03385 [math.GM], 2017.

FORMULA

a(n) = floor(log_2(3^n)) = log_2(A000244(n)-A056576(n)) = a(n-1)+A022921(n-1).

a(n) = A020914(n) - 1. - L. Edson Jeffery, Dec 12 2014

EXAMPLE

a(3)=4 because 3^3=27 and 2^4=16 is power of 2 immediately below 27.

MAPLE

seq(ilog2(3^n), n= 0 .. 1000); # Robert Israel, Dec 11 2014

MATHEMATICA

Table[Floor[Log[2, 3^n]], {n, 0, 69}] (* Robert G. Wilson v, Apr 06 2006 *)

Table[Floor[n*Log[2, 3]], {n, 0, 68}] (* L. Edson Jeffery, Dec 11 2014 *)

PROG

(PARI) {a(n) = if( n<0, 0, logint(3^n, 2))}; /* Michael Somos, Dec 13 2014 */

(Haskell)

a056576 = subtract 1 . a020914  -- Reinhard Zumkeller, May 17 2015

CROSSREFS

Cf. A000079 (powers of 2), A000244 (powers of 3), A020914, A022921.

Cf. A056850, A117630 (complement), A020857 (decimal expansion of log_2(3)), A076227, A100982.

Sequence in context: A054385 A284773 A172272 * A182770 A059552 A047516

Adjacent sequences:  A056573 A056574 A056575 * A056577 A056578 A056579

KEYWORD

nonn

AUTHOR

Henry Bottomley, Jun 29 2000

STATUS

approved

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Last modified May 21 22:24 EDT 2019. Contains 323467 sequences. (Running on oeis4.)