login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A020914 Number of digits in base 2 representation of 3^n. 24
1, 2, 4, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 89, 91, 92, 94, 96, 97, 99, 100, 102, 104, 105, 107 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also, numbers n such that the first digit in ternary expansion on 2^n is 1. - Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006

a(n) is the smallest integer such that n/a(n) < log_2 (3). - Trevor G. Hyde (thyde12(AT)amherst.edu), Jul 31 2008

This sequence represents allowable values of the "dropping time" in the Collatz (3x+1) problem when iterated according to the function f(n) := n/2 if n is even, (3n+1)/2 otherwise, as tabulated in A126241. There is one exception which is A126241(1), which has been set to zero by convention. - K. Spage, Oct 22 2009

An integer (x) is a member of A020914 if and only if floor(x*(1+log(2)/log(3))) - abs(x-1)*(1+log(2)/log(3)) - 1 >= 0. - K. Spage, Oct 22 2009

Also smallest k such that ceil(2^k /3^n) = 2. - Michel Lagneau, Jan 31 2012

a(n) = A070939(A000244(n)) = length of n-th row in triangle A227048. - Reinhard Zumkeller, Jun 30 2013

For n>0, first differences of A022330. - Michel Marcus, Oct 03 2013

Also the number of powers of two less than or equal to 3^n. - Robert G. Wilson v, May 25 2014

Except for 1, A020914 is the complement of A054414 and therefore these two form a pair of Beatty sequences. - Robert G. Wilson v, May 25 2014

A020915(a(n)) = n + 1. - Reinhard Zumkeller, Mar 28 2015

REFERENCES

Mike Winkler, On the structure and the behaviour of Collatz 3n+ 1 sequences, 2014; http://mikewinkler.co.nf/collatz_structure_2014.pdf

LINKS

T. D. Noe, R. J. Mathar, Table of n, a(n) for n = 0..20000

M. Winkler, New results on the stopping time behaviour of the Collatz 3x + 1 function, arXiv:1504.00212 [math.GM], 2015.

FORMULA

a(n) = floor(1+n*log(3)/log(2)) - K. Spage, Oct 22 2009

a(0) = 1, a(n+1) = a(n) + A022921(n). - K. Spage, Oct 23 2009

a(n) = A122437(n-1) - n. - K. Spage, Oct 23 2009

A098294(n) = a(n) + n for n > 0. - Mike Winkler, Dec 31 2010

a(n) = 1 + floor(n*log_2(3)) = 1 + A056576(n) = 1 + floor(n*A020857). - L. Edson Jeffery, Dec 12 2014

MAPLE

A020914 :=n->nops(convert(3^n, base, 2)):

seq(A020914(n), n=0..70); # Emeric Deutsch, Apr 30 2006

seq(ilog2(3^n)+1, n=0 .. 100); # Robert Israel, Dec 12 2014

MATHEMATICA

Table[Length[IntegerDigits[3^n, 2]], {n, 0, 100}] (* Stefan Steinerberger, Apr 19 2006 *)

Do[If[First[IntegerDigits[2^n, 3]] == 1, Print[n]], {n, 1, 100}] (* Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006 *)

f[n_] := Floor[ Log2[3^n] + 1]; Array[f, 105, 0] (* Robert G. Wilson v, May 25 2014 *)

PROG

(PARI) for(n=0, 100, print1(floor(1+n*log(3)/log(2)), ", ")) \\ K. Spage, Oct 22 2009

(Haskell)

a020914 = a070939 . a000244  -- Reinhard Zumkeller, Jun 30 2013

CROSSREFS

Cf. A056576, A054414, A070939, A000244, A227048, A022330, A022921, A126241.

Cf. A020857 (decimal expansion of log_2(3)).

Cf. A020915.

Sequence in context: A285401 A139449 A204399 * A195176 A195126 A047496

Adjacent sequences:  A020911 A020912 A020913 * A020915 A020916 A020917

KEYWORD

nonn,base,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Stefan Steinerberger, Apr 19 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.