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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A050603 A001511 with every term repeated. 7
1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 5, 5, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 6, 6, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 5, 5, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Column 2 of A050600: a(n) = add1c(n,2).

Absolute values of A094267.

Consider the Collatz (or 3x+1) problem and the iterative sequence c(k) where c(0)=n is a positive integer and c(k+1)=c(k)/2 if c(k) is even, c(k+1)=(3*c(k)+1)/2 if c(k) is odd. Then a(n) is the minimum number of iterations in order to have c(a(n)) odd if n is even or c(a(n)) even if n is odd. - Benoit Cloitre, Nov 16 2001

LINKS

James Spahlinger, Table of n, a(n) for n = 0..10000

Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu, A growth model based on the arithmetic Z-game, arXiv:1511.04315 [math.NT], 2015.

FORMULA

Equals A053398(2, n).

G.f.: (1+x)/x^2 * Sum(k>=1, x^(2^k)/(1-x^(2^k))). - Ralf Stephan, Apr 12 2002

a(n) = A136480(n+1). - Reinhard Zumkeller, Dec 31 2007

a(n) = A007814(n + 2 - n mod 2). - James Spahlinger, Oct 11 2013, corrected by Charles R Greathouse IV, Oct 14 2013

a(2n) = a(2n+1). 1 <= a(n) <= log_2(n+2). - Charles R Greathouse IV, Oct 14 2013

a(n)=A007814(n+1)+A007814(n+2).

a(n) = (-1)^n * A094267(n). - Michael Somos, May 11 2014

PROG

(PARI) a(n)=valuation(n+2-n%2, 2) \\ Charles R Greathouse IV, Oct 14 2013

(PARI) {a(n) = my(A); if( n<0, 0, A = sum(k=1, length( binary(n+2)) - 1, x^(2^k) / (1 - x^(2^k)), x^3 * O(x^n)); polcoeff( A * (1 + x) / x^2, n))}; /* Michael Somos, May 11 2014 */

CROSSREFS

Bisection gives column 1 of A050600: A001511.

Cf. A007814, A094267.

Sequence in context: A003638 A094267 A136480 * A286554 A037162 A278566

Adjacent sequences:  A050600 A050601 A050602 * A050604 A050605 A050606

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen Jun 22 1999

EXTENSIONS

Definition simplified by N. J. A. Sloane, Aug 27 2016

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 February 24 05:37 EST 2018. Contains 299597 sequences. (Running on oeis4.)